Data Handling - Class 8 Maths - Extra Questions

Which of the following have equally likely outcomes?
Explain
Mr Sharma has one child. The child is either a boy or a girl.

Equally likely outcomes: When all the outcomes in sample space have the same probability, outcomes are called equally likely outcomes. Birth of a boy or a girl has an equal probability. Now Mr Sharma has one child. The child is a boy, or a girl has an equal probability and hence it is an equally likely outcomes.


A die is thrown. Write the sample space. If $$B$$ is the event of getting an even number, write the event $$B$$ using set notation.

A die is throws.
$$\therefore$$ Sample space $$(S)=\left\{ 1,2,3,4,6 \right\} $$
$$\therefore$$ $$n(S)=6$$
Let $$B$$ is the event that the number is even.
$$B=\{2,4,6\}$$
$$\therefore$$ $$n(B)=3$$


A card is drawn from the pack of $$25$$ cards labelled with numbers $$1$$ to $$25$$. Write the sample space for this random experiment.

Let S be sample space of the experiment.
Then, the sample will contain all the cards that can be drawn out.
$$\Rightarrow S=\left \{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25\right\}$$


A die if thrown once. Find the probability of getting a number less than $$5$$.

Total possibilities $$=6$$
Favourable possibilities $$=(1, 2, 3, 4)=4$$
$$\Rightarrow$$ Probability $$=\dfrac{4}{6}=\dfrac{2}{3}$$.

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When a die is thrown, list the number of outcomes of an event of getting a number greater than $$5$$.

In a throw of die, the total outcomes are $${1,2,3,4,5,6}$$
A number greater than $$5$$ is $$6$$.

Hence, only $$1$$ outcome possible.


Toss a coin for number of times as shown in the table. And record your findings in the table.
Number of TossesNumber of headsNumber of tails
          10
          20
          30
          40
          50
What happens if you increase the number of tosses more and more.

 Number of tossesNumber of headsNumber of tails
1064
20128
301218
401822
502723
On increasing the number of tosses the chances of getting heads and tails will get equal.


Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

When a coin is tossed, there is an equally likely outcome of getting either a head or a tail, so tossing a coin is a fair way of deciding.


Which of the following experiments have equally likely outcomes? Explain.
(i) A driver attempts to start a car. The car starts or does not start.
(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.
(iii) A trial is made to answer a true-false question. The answer is right or wrong.
(iv) A baby is born. It is a boy or a girl

i) The car getting started or not started depends on how old the car is, is their fuel in the engine, is has met in an accident etc.
so, the factors on which the car will start or not is not the same in both cases.
Therefore,it is not an equally likely event.

ii) The amount of shots he/she shoots can go in more times than it misses or vice-versa depending on player ability. which is not specified here.
Therefore,it is not an equally likely event.

iii) The answer can only be right or wrong. it is equally likely that answer is right or wrong because it is a true false question.
Therefore,it is an equally likely event.

iv) A baby can be boy or girl. it is equally likely that the baby is a boy or a girl.
Therefore,it is an equally likely event.

Hence, The option $$(iii)$$ and $$(iv)$$ are equally likely outcomes


A die is thrown. If $$A$$ is an event of getting an odd number, then write the sample space and event $$A$$ in set notation.

Let $$S$$ be sample space. Then,
$$S=\left\{1,2,3,4,5,6\right\}$$
$$A$$ is the event of getting an odd number.
$$A=\left\{1,3,5\right\}$$


There are $$30$$ tickets numbered from $$1$$ to $$30$$ in a box and a ticket is drawn at random. If $$A$$ is the event that the number on the ticket is a perfect square, then write the sample space $$S$$, $$n(S)$$, the event $$A$$ and $$n(A)$$.

Given that there are $$30$$ tickets in a box and a ticket is drawn:
If $$S$$ be the sample space,
$$S=\left\{ 1,2,3,.......30 \right\} $$
Number of elements in $$S$$:
$$\therefore$$ $$n(S)=30$$

If $$A$$ be the event that the ticket bears a number which is a perfect square,
$$A=\left\{ 1,4,9,16,25 \right\} $$
Number of elements in $$A$$:
$$\therefore$$ $$n(A)=5$$


A die is thrown. Write the sample space. If $$P$$ is the event of getting an odd number, then write the event $$P$$ using set notation.

A die is thrown
$$\therefore $$ $$S=\left\{ 1,2,3,4,5,6 \right\} $$
$$\therefore $$ $$n(S)=6$$
Let $$P$$ is the event of getting an odd number.
$$\therefore$$ $$P=\left\{ 1,3,5 \right\} $$
$$\therefore$$ $$n(P)=3$$


A die is thrown. If $$A$$ is the event that the number on upper face is less than $$5$$, then write sample space and event $$A$$ in set notation.

A die is thrown.
Total outcomes: $$6$$
Sample Space: $$ = \{1,2,3,4,5,6\}$$
$$A:$$ An event that the number on upper face is less than $$5$$
$$A:\{1,2,3,4\}$$


A die is thrown. Write the sample space. If $$A$$ is the event that the number is a perfect square, write the event $$A$$ using set notation.

A die is thrown
$$\therefore$$ Sample space$$S=\left\{ 1,2,3,4,5,6 \right\} $$
$$\therefore$$ $$n(S)=6$$
Let $$A$$ be the event that the number is a perfect square
$$\therefore$$ $$A=\left\{ 1,4 \right\} $$
$$\therefore$$ $$n(A)=2$$


There are $$30$$ tickets in a box numbered from $$1$$ to $$30$$. A ticket is drawn out at random. Let $$A$$ be the event that the number on the ticket is a multiple of $$6$$. Write the sample set $$S$$ and outcomes of event $$A$$ in set form.

There are $$30$$ tickets in a box
A ticket is drawn
Sample space $$(S)=\left\{ 1,2,3,4,5,......30 \right\} $$
$$n(S)=30$$
Let $$A$$ is the event that the number is a multiple of $$6$$
$$\therefore$$ $$A=\left\{ 6,12,18,24,30 \right\} $$
$$\therefore$$ $$n(A)=5$$


A die is thrown. If $$A$$ is the event that the number on upper face is an even, then write sample space and event $$A$$ in set notation.

Let $$S$$ be the sample space of throwing a die
Then, $$S = \{1, 2, 3, 4, 5, 6\}$$
Let $$A$$ be the event that the number on upper face is an even.
$$A = \{2, 4, 6\}$$


A die is thrown. If $$A$$ is the event that the number on upper face is a prime, then write sample space and event $$A$$ in set notation.

Let $$S$$ be the sample space of throwing a die
Then, $$S =\{1, 2, 3, 4, 5, 6\}$$
Let $$A$$ be the event of getting a prime number
$$A = \{2, 3, 5\}$$


There are $$30$$ tickets numbered from $$1$$ to $$30$$ in a box. A ticket is drawn at random. If $$A$$ is the event that the number on the ticket is a prime number less than $$15$$, write the sample space $$S$$, $$n(S)$$ the event $$A$$ and $$n(A)$$.

Given, there are $$30$$ tickets in a box. A ticket is drawn at random.

Let $$S$$ be the sample space,
$$S=\left\{ 1,2,3,4,.........,30 \right\} $$
$$n(S)=30$$

By considering the given defination of event $$A,$$
$$A=\left\{ 2,3,5,7,11,13 \right\} $$
$$n(A)=6$$


A die is thrown. Write the sample space. If $$A$$ is the event that the number is less than four, write the event $$A$$ using set notation.

A die is thrown
$$\therefore$$ Sample space $$S=\left\{ 1,2,3,4,5,6 \right\} $$
$$n(S)=6$$
Let $$A$$ is the event that the number is less than four,
$$A=\left\{ 1,2,3 \right\} $$
$$n(A)=3$$


There are $$30$$ tickets numbered from $$1$$ to $$30$$ in a box. A ticket is drawn at random from the box and if $$A$$ is the event that the number on the ticket is a multiple of five, write the sample space $$S$$, $$n(S)$$, the event $$A$$ and $$n(A)$$.

There are $$30$$ tickets in a box.
Sample space $$(S)=\left\{ 1,2,3,4,.........,30 \right\} $$
$$n(S)=30$$
Let $$A$$ is the event that the number on the ticket is a multiple of $$5$$
$$\therefore$$ $$A=\left\{ 5,10,15,20,25,30 \right\} $$
$$\therefore$$ $$n(A)=6$$


Two coins are tossed simultaneously. Write the sample space $$'S'$$ and the number of sample point $$n(S)$$. $$A$$ is the event of getting no head. Write the event $$A$$ in set notation and find $$n(A)$$.

Sample space $$S = \left \{(H, H), (H, T), (T, H), (T, T)\right \}$$
Number of sample space $$n(S) = 4$$
$$D =$$ getting no head
$$D = \left \{(T, T)\right \}$$
$$n(D) = 1$$


Two coins are tossed simultaneously. Write the sample space $$S$$ and the number of sample point $$n(S)$$. $$A$$ is the event of getting at least one head. Write the event $$A$$ in set notation and find $$n(A)$$

Sample space $$S = \left \{(H, H), (H, T), (T, H), (T, T)\right \}$$
Number of sample space $$n(S) = 4$$
$$A =$$ Getting at least one head
$$A = \left \{(H, H), (H, T), (T, H)\right \}$$
$$n(A) = 3$$


A die is thrown then write the sample $$S$$ and number of sample points $$n(S)$$ and also write event $$A$$ of getting a perfect square on the upper face write $$n(A)$$

$$S=\left\{1,2,3,4,5,6\right\}$$
$$n(S)=6$$
$$A=\left\{1,4\right\}$$
$$n(A)=2$$


Form $$2$$ digit number using $$0, 1, 2, 3, 4, 5$$ without repeating the digits. Write the sample space $$S$$, number of sample points $$n(S), U, n(U)$$ for $$U$$ is the event that the number so formed is divisible by $$5$$.

The sample space is
$$S= \{10, 12, 13, 14, 15, 20, 21, 23, 24, 25, 30, 31, 32, 34, 35, 40, 41, 42, 43, 45, 50, 51, 52, 53, 54\}$$
$$\therefore  n(S) = 25$$
Now $$U$$ is event that the number so formed is divisible by $$5$$.
$$\therefore U = \{10, 15, 20, 25, 30, 35, 40, 45, 50\}$$
$$\therefore  n(U) = 9$$


I read $$\dfrac{3}{7}$$ pages of a book containing 100 pages. Lalita read $$\dfrac{2}{5}$$of the same book. who read less ?

Comparing 

$$\dfrac {3}{7}\,\,\,\,\,\,\,\,\,\,\,\,\, \dfrac {2}{5}$$

$$\dfrac {15}{35} > \dfrac {14}{35}$$

$$\therefore $$  Lalita  read less 

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The maximum and minimum temperatures of five Indian cities are given in $$C^\circ.$$ Draw a joint bar graph for this data.
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$$2$$   $$5$$   $$6$$   $$8$$   $$2$$   $$6$$   $$3$$   $$9$$
For the numbers in the list, write down
(a) the range
(b) the mode
(c) the median

Given data is $$2,5,6,8,2,6,3,9$$
$$a) $$ The maximum and minimum numbers in this data is $$9,2$$ respectively
So range is $$9-2=7$$
$$b)$$ The most repeated number in this data is $$2,6$$
So modes are $$2,6$$
$$c)$$ The ascending order of the data is $$2,2,3,5,6,6,8,9$$
So median is $$\dfrac{5+6}{2}=5.5$$


Write all the possible outcomes for the occurrence of a number 4   when a fair die is tossed.

Sample space is the set of collection of all possible outcomes of an Event
The sample space of a fair die is 
$$S=\{1,2,3,4,5,6\}$$


Three coins are tossed once. Find the probability of getting exactly two tails?

Total number of outcomes $$=(HHH),(HHT),(HTH),(THH),(TTH),(TTT),(THT),(HTT)=8$$
 exactly two tails $$(HTT),(TTH),(THT)$$
$$n=3$$
P(exactly two tails)$$=\dfrac{3}{8}$$


When a dice is thrown, outcomes $$ 1, 2,3,4,5, 6 $$ are equally ______

The correct fill up is $$\underline{\text{likely}}$$.


The bar graph as shown in above figure represents the heights (in cm) of 50 students of Class XI of a particular school. Study the graph and answer the following questions:
How many students are in the range of shortest height of the class?
1671030_6d8c1b0692764b9abcc03a158a144264.png

The minimum range of height is $$140-145$$cm.
The number of students that are in the range of shortest height of the class $$= 7$$



An experiment whose outcomes cannot be predicted exactly in advance is called a_______ experiment.

The correct fill up is random.
When the outcomes of an experiment cannot be predicted, it is called as a random experiment.


Each outcome or a collection of outcomes in an experiment makes an _______

The correct fill up is event.
The set of outcomes of an experiment is termed as an event.


Read the above bar graph and answer the following question:
Which state has the total production of wheat and rice minimum?
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Consider a chart by using data from the bar graph:
 $$States$$   $$Rice\, production$$ $$Wheat \,production$$ $$Total\, production$$ 
 $$U.P$$    $$8$$    $$16$$     $$24$$
$$W.P$$  $$10$$    $$2$$   $$12$$
 $$M.P$$ $$5$$      $$5$$ $$10$$
 $$Maharashtra$$ $$4$$   $$2$$    $$6$$
 $$Haryana$$   $$3$$   $$6$$  $$9$$
Maharashtra has the total production of wheat and rice minimum.


When a dice is rolled, the six possible outcomes are______.


Each face of a die has unique value of integer ranging from $$1$$ to $$6$$

Thus number of possible outcomes are $$(1,2,3,4,5,6)$$


In a simultaneous throw of a pair of dice, find the probability of getting a total more than $$7$$.

n(S) = 6 X 6 = 36
E = { (2,6) ; (6,2) ; (3,5); (5,3); (4,4) ; (4,5) ;(5,4); (4,6); (6,4) ; (5,5) ; (3,6) ; (6,3) ; (5,6) ;(6,5) ; (6,6) }
$$ \displaystyle \Rightarrow n(E)= 15 $$
$$ \displaystyle \Rightarrow P(E)= \frac{15}{36}=\frac{5}{12} $$
$$ \displaystyle \frac{5}{12} $$


In a throw of coin, find the probability of getting a head.

Here S = { H,T} ; E = {H}
 $$ \displaystyle \therefore  P(E) = \frac{n(E)}{n(S)} $$
 $$ \displaystyle = \frac{1}{2} $$


An unbiassed coins are tossed. Find the probability of getting at most one head.

S = {HH,HT,TH,TT}
$$ \displaystyle  \Rightarrow n(S)=4 $$
E= event of getting at the most one head
= { TT, HT, TH}
$$ \displaystyle  \Rightarrow n(E)=3 $$
$$ \displaystyle  \therefore n(E)=\frac{n(E)}{n(S)} = \frac{3}{4} $$


An unbiassed die is toossed. Find the probability that it is a multiple of $$3 $$. 

S = { 1, 2, 3, 4, 5, 6}
$$\displaystyle \Rightarrow $$ n(S)=6
E={3, 6}
$$\displaystyle \Rightarrow $$ n(E)=2
$$\displaystyle \therefore  $$ P(E)=$$\displaystyle \frac{2}{6}=\frac{1}{3}$$


Two coins are tossed simultabeously. Find the probability of getting:
(i) at least one Tail
(ii) atmost two Head
(iii) one Head

Total outcomes when two coins are tossed $$= HH, HT, TH, TT$$
(i) Favorable $$= HT, TT, TH \Rightarrow P = \dfrac{3}{4}$$
(ii) Favorable $$=HH, HT, TH, TT \Rightarrow P = \dfrac{4}{4} = 1$$
(iii) Favorable $$= HT, TH \Rightarrow P = \dfrac{2}{4} = \dfrac{1}{2}$$

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In a cricket match, a batswoman hits a boundary $$6$$ times out of $$30$$ balls she plays. Find the probability that she did not hit a boundary.

Number of times the batswoman hit a boundary $$= 6$$  (given)
Total balls she played$$= 30$$

Probability (hitting a boundary) $$= \dfrac{\text {Number of times she hit a boundary}}{\text{Total number of balls she played}}=\dfrac{6}{30} $$

Probability (hitting a boundary)$$= \dfrac{1}{5}$$

Probability of not hitting a boundary $$= 1-$$Probability (hitting a boundary)
                                                              
                                                             $$=1- \dfrac{1}{5} = \dfrac{4}{5}$$


If a coin is tossed 3 times, then  the number of outcomes will be?

When a coin is tossed once, there are two possible outcomes - $$Head(H)$$ and $$Tail(T)$$
Hence, when a coin is tossed 3 times, the number of possible outcomes.
$$= 2*2*2 = 8.$$
The possible outcomes are 
{$$HHH, HHT, HTH, HTT, THH, THT, TTH, TTT$$} 


Two-digit numbers are formed using the digits $$0, 1, 2, 3, 4, 5$$ where digits are not repeated.
$$\text{P}$$ is the event that the number so formed is even.
$$\text{Q}$$ is the event that the number so formed is greater than $$50$$.
$$\text{R}$$ is the event that the number so formed is divisible by $$3$$.
Then write the sample space $$\text{S}$$ and events $$\text{P, Q,} $$ and $$ \text{R}$$ using set notation.

$$\text{S}=\left\{10,12,13,14,15,20,21,23,24,25,30,31,32,34,35,40,41,42,43,45,50,51,52,53,54\right\}$$
$$\text{P}=\left\{10,12,14,20,24,30,32,34,40,42,50,52,54\right\}$$
$$\text{Q}=\left\{51,52,53,54\right\}$$
$$\text{R}=\left\{12,15,21,24,30,42,45,51,54\right\}$$


Suppose that the letter cards for the word $$MATHEMATICS$$ were put face down and mixed up and a card is picked up at random. What is the probability of picking up a vowel?

Total no. of words in MATHEMATICS$$=11$$
No. of vowels in it $$=4$$
$$\therefore$$ Probability $$=\dfrac{4}{11}$$.


From a group of $$2$$ men and $$3$$ women, two persons are selected. Describe the sample space of the experiment. If $$E$$ is the event in which one man and one woman are selected, then which are the cases favourable to $$E$$ ?

Let 2 men be $$ M_{1}, M_{2}$$ & 3 women be $$ W_{1}, W_{2}, W_{3}.$$ Let s be sample 
space for selecting 2 persons
$$ S = \left \{ (M_{1},M_{2}), (M_{1},W_{1}) (M_{1},W_{2})(M_{1}, W_{3}),(M_{2}, W_{1})(M_{2}, W_{2}) (M_{2}, W_{3}),(W_{1},W_{2})(W_{1}, W_{3}), (W_{2}, W_{3}) \right \}$$
cases favourable to event in which 1 man  & 1 woman are selected
$$ =(M_{1},W_{1}), (M_{1}, W_{2}), (M_{1},W_{3}), (M_{2},W_{1}) ,(M_{2},W_{2}), (M_{3}, W_{3}) $$


There are $$5$$ cards in a box with numbers $$1\ to 5$$ written on them. If $$2\ cards$$ are picked out from the box, write all the possible outcomes and find the probpossible  ability of getting both even numbers. 

Possible outcomes are:$$(1,2),(1,3),1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,4)$$
Total sample space$$=10$$
Probability of getting both no. even$$=\cfrac{1}{10}$$


Three different coins are tossed together find the probability of .
i) Exactly two heads             ii) At least one tails 
ii) Almost two heads             iv) At most two tails 
v) At least two tails               vi) At most one head 
vii) At least one head

Total possible outcomes are 

$${ TTT, TTH , THT, THH, HTT, HTH, HHT, HHH }$$

Number of total possible outcomes= $$8 $$

i) Exactly two heads 

$${ THH,  HTH, HHT }$$      

$$=\dfrac{3}{8}$$   

ii) At least one tails 

$${ THH, HTH, HHT }$$

$$=\dfrac{3}{8}$$

iii) Almost two heads             

$${THH, HTH, HHT, HHH }$$

$$=\dfrac{4}{8}=\dfrac{1}{2}$$

iv) At most two tails 

$${TTT, TTH , THT,  HTT }$$

$$=\dfrac{4}{8}=\dfrac{1}{2}$$

v) At least two tails               

$${ TTH , THT,  HTT }$$

$$=\dfrac{3}{8}$$

vi) At most one head 

$${ TTH , THT, THH, HTT, HTH, HHT }$$

$$=\dfrac{6}{8}=\dfrac{3}{4}$$

vii) At least one head

$${TTH , THT,  HTT }$$

$$=\dfrac{3}{8}$$



What is the probability of obtaining total outcome in the multiple of $$12$$ if two die is tossed together once.

If the two dice are casino-type dice, then the only way to get a multiple of 12 is the result (6,6). This is a multiple of 12 because  $$6+6=12=1\times 12$$.

So, with a sample space of $$6\times 6=36$$ outcomes,

P(getting a multiple of 12 when two dice are tossed together)=136


A die has six faces numbered from $$1$$ to $$6$$. It is rolled and number on the top face is noted. When this is treated as random trial.
(a) What are the possible outcomes?
(b) Are they equally likely? Why?
(c) Find the probability of a composite number turning up on the top face.

(a) Possible outcomes $$=\{1,2,3,4,5,6\}$$
(b) All of them having probability $$=\dfrac{1}{6}$$
     So, they have equal chances
(c) Composite numbers between 1 to 6 $$=\{4,6\}$$
     Probability $$=\dfrac{2}{6}=\dfrac{1}{3}$$


Roll a die ten times and record the outcomes in the form of table.

 Sl.No outcomes
1 6 
 26 
 34 
 41 
 56 
 65 
 72 
 81 
 96 
 103 

Here a total of ten outcomes are noted in a table form. 
The total number of possible outcomes could be form 1 to 6. 
Here 4 times the result was 6; 1 time it was 5; 1 time it was 4, 1 time it was 3, 1 time it was 2 and 2 times it was 1.


In a two child family, one child is a boy. What is the probability that the other child is a girl?

Given in a two child family that one child is a boy.

Then the chance of the other child being a girl is $$\dfrac {1}{2}$$


A bag contains $$4$$ identical red balls and $$3$$ identical black balls. The experiment consists of drawing one ball, then putting it into the bag and again drawing a ball. What are the possible outcomes of the experiment?

A bag contain 4 red balls and 3 black balls 
Let us assumed Red = R
Let us assume black = B
Now, a ball drawn is first attempt, so elementary event is 
$$S_1 = \{R, B\}$$

And, the bag will put into the bag and draw again, then the elementary events are
$$S_2 = \{R, B\}$$

Thus, the total sample space associated is 
$$S = S_1 , S_2$$

$$S = \{RR, RB, BR, BB\}$$

Hence, S is the sample space for the given experiment.


The population of Delhi State in different census years is as given below:
Census year19611971198119912001
Population in Lakhs305570110150
Represent the above information with the help of a bar graph.


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Read the following bar graph and answer the following questions:
What is the information given by the bar graph?
1670953_84a52df3fca24f2aa2d90e0f4285c6f9.png

Number of government companies in India during some years.


Read the following bar graph and answer the following questions : What information is given by the bar graph ? 
1670990_20d1bc83b6a844cb9900b6ed3c7bc7dd.png

It gives the information regarding import and export from 1982-83 to 1986-87


The bar graph shown in above figure represents the circulation of newspapers in 10 languages.
study the bar graph and answer the following question:
State the language in which the smallest number of newspapers are published.
1671079_889d98bd04df4a3484337ae55f0c1024.png

Punjabi is the language in which the smallest number of newspapers are published from the graph.



Read the following bar graph (Fig. 23.15) and answer the following questions:
What is the minimum and maximum productions of cement and corresponding years?
1671053_bc60169feccf49dcb41183aeda4a182e.png

Minimum: 30 Lakh tonnes, 1950-51,
Maximum: 232 lakh tonnes, 1982-83


The following table gives the route length (in thousand kilometers) of the Indian Railway in some of the years :
Year1960 - 611970 - 711980 - 811990 - 91 2000 - 2001
Route length (in thousand km )5660617498
Represent the above with the help of of a bar graph.


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The following data gives the number (in thousands) of applicants registered with an Employment Exchange during, 1995-2000 :
Year199519961997199819992000
Number of applicants 
registered (in thousands )		182024283034
Construct a bar graph to represent the above data.


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The production of saleable steel in some of the steel plants of our country during 1999 is given below:
PlantBhilaiDurgapurRourkelaBokaro
Production
(In thousand tonnes )		16080200150
Construct a bar graph to represent the above data on a graph paper by using the scale 1 big divisions = 20 thousand tonnes.


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The bar graph shown in Fig.16 represents the circulation of newspapers in 10 languages.
study the bar graph and answer the following question:
Name two pairs of languages which publish the same number of newspapers.
1671076_393e370c22974d9db023bdf699a9877b.png


1671117_1671076_ans_26c722d2fca14606a5821db2e1f0779b.jpg


The following data gives the number (in thousands) of applicants with an Employment Exchange during, 1995-2000 :
Year199519961997199819992000
Number of applicants 
registered (in thousands )		182024283034
Construct a bar graph to represent the above data.


1671115_1671064_ans_35d7e3f81d8e46eab223208b7a800ad0.jpg


Read the following bar graph (Fig. 23.15) and answer the following questions:
What was the production of cement in the year 1980-81?
1671049_190d3b55fc9d474c8c9933d110ac6c61.png


1667250_1671049_ans_194b5de25c0541bea5ee562af011039e.jpg


Read the bar graph given in above figure and answer the following question:
What information is given by the bar graph?
1671095_0c8d4bc5b9d3406b8b3f55b7320d2c26.png


1671120_1671095_ans_114e45684855418f852daea9af335739.jpg


Read the bar graph shown in fig. and answer the following question:
Of which state, were the minimum number of tickets sold?
1675389_1bbb40dba0e0481ba17e0dd886b979ed.png

Minimum (20) number of tickets were sold of Rajasthan.


Read the following bar graph and answer the following questions:
In which year the difference of the values of export and import is maximum?
1675403_c50a32b004214ed1a19945378a9c8313.png

From the bar graph,
The diffence (in $$100$$ crore of rupees) between the values of export and import are as follows,
for the year $$1982-83$$, difference $$=14-8=6$$
for the year $$1983-84$$, difference $$=18-10=8$$
for the year $$1984-85$$, difference $$=19-12=7$$
for the year $$1985-86$$, difference $$=20-11=9$$
for the year $$1986-87$$, difference $$=22-10=12$$

Hence, the difference between the values of import and export is maximum in the year $$1986-87$$.


Study the bar graph representing the number of persons in various age groups in a town shown in Fig.. Observe the bar graph and answer the following questions:
What is the age-group of exactly $$1200$$ persons living in the town?

1675430_c16d9fed8f954d9dac5eb109006b5a33.png

Observing bar graph,
Age group of $$20-25$$ have $$1200$$ persons exactly.


The following data gives the amount of manure (in thousand tonnes) manufactured by a company during some years:
Year199219931994199519961997
Manure (in thousand tonnes)153545304020
Represent the above data with the help of a bar graph.

Given data gives the amount of manure(in thousand tonnes) manufactured by a company during some years
Year                                            $$1992$$           $$1993$$          $$1994$$            $$1995$$             $$1996$$               $$1997$$
Manure(in thousand tonnes)      $$15$$                $$35$$              $$45$$                $$30$$                 $$40$$                     $$20$$

1480924_1675575_ans_3cfe1bb9a5c14d46b50588bd04c67cda.png


The following data gives the amount of loans (in crores of rupees) disbursed by a bank during some years:
Year19921993199419951996
Loan (in crores of rupees)2833555580
Represent the above data with the help of a bar graph.

The amount of loans(in crores of rupees) disturbed by a bank-during some years
Year                                         $$1992$$          $$1993$$          $$1994$$          $$1995$$           $$1996$$
Loan(in crores of rupees)       $$28$$                $$33$$               $$55$$               $$55$$              $$80$$

1480698_1677197_ans_9228e0d1634149d0ade9a99028062003.png


The following data gives the number (in thousands) of applicants registered with an Employment Exchange during. $$1995-2000$$:
Year$$1995$$$$1996$$$$1997$$$$1998$$$$1999$$$$2000$$
Number of applicants registered (in thousands)$$18$$$$20$$$$24$$$$28$$$$30$$$$34$$
Construct a bar graph to represent the above data.

Given that
the number (in thousand) of applicant's registered with an employment Exchange during $$1995-2000$$

 Year1995  1996 1997 1998 1999 2000
No of applicants registered (in thousand) 18 20 24 28 30 34

2129254_1677192_ans_daef3393b555441ebfa777c28b2ef2cd.png


The production of saleable steel in some of the steel plants of our country during 1999 is given below:
PlantBhilaiDurgapurRourkelaBokaro
Production (In thousand tonnes)16080200150
Construct a bar graph to represent the above data on a graph paper by using the scale 1 big division = 20 thousand tonnes.

Given that
the production of salesble steel in some of the steel
plants of our country during $$1999$$ is
Plant                                                    Bhilai            Durgapur           Rourkela             Bokaro
Production(in thousand tonnes)         $$160$$                   $$80$$                    $$200$$                     $$150$$

1479301_1677191_ans_121ad9c18bfc450a86718f66433088d9.png


Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that sum of the two numbers appearing on the top of the dice is
$$8$$

$$(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)$$
$$(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)$$ 
$$(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)$$ 
$$(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)$$
$$(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)$$
$$(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)$$
Total outcomes $$=36$$
Sum is $$8$$
Favourable outcomes $$=(2,6), (3,5), (4,4), (5,3), (6,2)=5$$
$$P$$ (sum is $$8$$) $$=\dfrac{5}{36}$$


The following table gives the route length (in thousand kilometres) of the Indian Railways in some of the years:
Year1960-611970-711980-811990-912000-2001
Route length (in thousand kilometres)5660617498
Represent the above data with the help of a bar graph.

The data gives the route length(in thousand kilometer) of the Indian Railways in some of the years.
Year                                                       $$1960-61$$          $$1970-71$$           $$1980-81$$           $$1990-91$$             $$2000-2001$$
Route length(in thousand kilometers)       $$56$$                      $$60$$                           $$61$$                          $$74$$                          $$98$$

1480681_1677196_ans_82a14103b90d4bac99d028dea8fd0885.png


From a well-shuffled deck of $$ 52 $$ cards, one card is drawn at random. What is the number of all possible outcomes?

We Know that the deck of cards has a total of $$ 52 $$ cards . So, they are $$ 52 $$ cards 
$$ \therefore $$ The possible outcomes are $$ 52 $$ cards. 


A die is rolled. If the outcome is an even number, what is the probability that it is a number greater than $$2$$?


1543735_1707823_ans_308992b61e4f481f8f0e6220f7e6254c.jpg


Two coins are tossed simultaneously. What are all possible outcomes?

We know that the coin has two sides head (H) and tail (T)
So the possible outcomes are $$ X^m $$ . (where $$ X $$  is the number of outcomes when a coin is tossed and $$ m $$ is number of coins)

When there are $$ 2$$ tails 
$$ \therefore \, 2^2 = 4 $$ i.e. head and tail 
$$ \therefore $$ The possible outcomes are HH , HT , TH , TT . 


A die is thrown. What are all possible outcomes?

We know that the die has $$6$$ faces  So , they are $$ 1 , 2 $$ and $$ 3 , 4 ,  5 , 6 $$ 
$$ \therefore $$ The possible outcomes are $$ 1 , 2 ,  3 , 4 ,5 , 6 $$ 


A coin is tossed. What are all possible outcomes?

We know that the coin has two sides head (H) and tail (T)
So the possible outcomes are $$ X^m $$ . (where $$ X $$  is the number of outcomes when a coin is tossed and $$ m $$ is number of coins)

$$ \therefore \, 2^1 = 2 $$ i.e. head and tail 
$$ \therefore $$ The possible outcomes are H and T . 


The following data gives the production of foodgrains (in thousand tonnes) for some years:
Year199519961997199819992000
Production (in thousand tonnes)120150140180170190
Represent the above data with the help of a bar graph.

Given data gives
the production of food grains(in thousand tonnes) for some years
Year                                                   $$1995$$       $$1996$$      $$1997$$      $$1998$$        $$1999$$         $$2000$$
Production(in thousand tonnes)      $$120$$         $$150$$         $$140$$        $$180$$           $$170$$           $$190$$


1480691_1677208_ans_441a67005d20477a9a7d1f67c29b1a9c.png


The lengths in km (rounded to nearest hundred)
of some major rivers of India are given below: 
Draw a bar graph to represent the above information.

1789418_bca38c41ebfa49d2a857f833e5d75ef6.png

Take the length of River on the vertical axis and name of River on
horizontal axis. 

1646256_1789418_ans_9837efd2a0b2478aaf3f3cb51b088b46.png


In Throwing a die the number of possible outcomes is 


1921929_1791845_ans_f2b70af6f4204c789284a4a8dffd3ada.jpg


In the experiment of tossing a coin one time, the outcome is either _____ or ______.

The correct fill up is head or tail.
A coin has only two faces, head and tail.


The total number of outcomes when a coin is tossed is ______

A coin hs $$2$$ sides, head and tail.
Hence, when we toss a coin, we can either get a head or a tail.

Hence, the total number of outcomes when a coin is tossed is $$2$$.


List the outcomes you can see in these experiments
Drawing a ball from the containing $$5$$ identical ball of different containing $$5$$ identical ball of different colours
1809240_ccdd54b0e7594f019f2083ade9dbadde.png

The outcomes in drawing a ball from a bag containing $$5$$ identical balls of different colours = White, Red, Blue, Green, Yellow


List the outcomes you can see in these experiments
Spinning a wheel
1809225_ecff7d2e0d2b49c5aece33517c33bf63.png

The outcomes in spinning wheel $$= \{A, B, C, D\}$$


Which of the following experiments have equality likely outcomes? Explain
A player attempts to shoot a basketball. She/he shoot or misses the shot.

It is not equally likely, If he shoots the basket the ball will drop inside the basket, or he will miss it, this depends upon the skill of the individual basket ball player.


Two dice are rolled together. Write all the possible outcomes and find the probability of getting
a doubtlet (the same number appearing on each of the die)

$$(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)$$
$$(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)$$
$$(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)$$
$$(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)$$
$$(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)$$
$$(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)$$
Total outcomes$$=36$$
Favourable outcomes $$(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)=6$$
$$P$$ (a doublet ( the same number appearing on each of the die )) $$=\dfrac{6}{36}=\dfrac{1}{6}$$


Which of the following experiments have equality likely outcomes? Explain
A driver attempts to start a car. The car starts or does not start.

Equally Likely Event:-Event that have same theoretical probability.
it's not equally likely Event as the car may have a mechanical breakdown or fuel problems or may be can be loose. So it depends upon a various thing, so it is not an equally likely event.


Which of the following have equally likely outcomes?
Explain
A player calls for a head in a toss of a coin. The coin shows up either heads or tails.

Equally likely outcomes: When all the outcomes in sample space have the same probability, outcomes are called equally likely outcomes. In a toss of a coin occurrence of head or tail have equally probabilities. Thus it has an equally likely outcomes of head and tail.


Which of the following have equally likely outcomes?
Explain
A batsman plays and misses a ball. The either hits the wickets or misses them.

Equally likely outcome; When all the outcomes in sample space have the same probability, outcomes are called equally likely outcomes. A player plays a ball and misses it. Now there are many possibilities of the path took by ball after being missed by batsman. Hence occurrence of ball hitting wicket is not an equally likely outcome with missing. As it may go to wicketkeeper or it may go pass wicket keeper, Thus there are many possibilities for the event.


Which of the following have equally likely outcomes?
Explain
An attempt was made to answer a true-false question.
The answer is correct or incorrect.

Equally likely outcome: When all the outcomes in sample space have the same probability, outcomes are called equally likely outcomes. For a True or False. Now the sample space of the attempt contains two possibilities True or False. There can be only one correct answer for the event. Hence there is equal possibilities of answer being correct or incorrect and therefore it is an equally likely outcome.


Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that sum of the two numbers appearing on the top of the dice is
$$13$$

$$(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)$$
$$(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)$$ 
$$(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)$$ 
$$(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)$$
$$(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)$$
$$(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)$$
Sum is $$13$$
Favourable outcomes $$=0$$
$$P$$ (sum is $$13$$) $$=0$$
Since the maximum sum that can be obtained is $$12$$.


Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that sum of the two numbers appearing on the top of the dice is
less than or equal to $$12$$?

$$(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)$$
$$(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)$$ 
$$(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)$$ 
$$(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)$$
$$(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)$$
$$(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)$$
Total outcomes $$=36$$
Less than or equal to $$12$$ Possible outcomes = All outcomes have sum less than or equal to $$12=36$$.
$$P$$( less than or equal to $$12$$) $$=36/36=1$$


A die of six faces marked with the integers $$1,2,3,4,5,6$$ one on each face. Is thrown twice in succession what is the total number of outcomes thus obtained?

Total number of outcomes can be obtain from twice throw of dice=6*6=36


Write the class size and class limits in each of the following: 
$$47,52,57,62,67,72,77,82,87,92,97$$ and $$102$$


1669533_1670846_ans_548257fad07e4fbeb2a223623e082197.png


The following data shows the average age of men in various countries in a certain year:
CountryIndiaNepalChinaPakistanU.K.U.S.A.
Average age (in years)565260507075
Represent the above information by a bar graph.

Given data shows
The average age of man in various countries in a certain year
Country                             India           Nepal           China           Pakistan             U.K        U.S.A
Average age(in years)       $$56$$               $$52$$                $$60$$                  $$50$$                    $$70$$           $$75$$

1480694_1677203_ans_ba5dc8a1b1aa4ca9a63c4c90269cb593.png


The performance of students in 1 st term and 2nd term is as given below. Draw a double bar graph choosing appropriate scale and answer the following:
Subject:English HindiMathsScienceS.Science
$$ 1^{st}$$ term:6772888173
$$ 2^{nd}$$ term:7065958575
Has the performance gone down in any subject?



1480644_1677181_ans_11af54bb98484745b444e354ce3716b0.jpg


The following data gives the amount of loans (in crores of rupees) disbursed by a bank during some years:
Year19921993199419951996
Loan(in crores of rupees)2833555580
Represent the above data with the help of a bar graph.

Given data
the amount of loans(in crores of rupees) distributed by a bank-during some years
Year                                         $$1992$$            $$1993$$             $$1994$$            $$1995$$           $$1996$$
Loan(in crores of rupees)       $$28$$                  $$33$$                  $$55$$                $$55$$              $$80$$
$$1995$$ year amount of loan is not increased over that of the proceding year.


1480851_1675535_ans_0e5eeab469544c33a0086bd688d38fda.png


The following data gives the production of food grains (in thousand tonnes) for some years:
Year199519961997199819992000
Production (in thousand tonnes)120150140180170190
 Represent the above data with the help of a bar graph.

Given data gives
the production of food grains(in thousand tonnes) for same years
Year                                                     $$1995$$           $$1996$$           $$1997$$           $$1998$$           $$1999$$            $$2000$$
Production(in thousand tonnes)         $$120$$             $$150$$            $$140$$             $$180$$                $$170$$              $$190$$.

1480919_1675562_ans_561d9dd6e4ab4b058f82c5b2eb9afe4c.png


The following table shows the interest paid by a company (in lakhs):
Year1995-961996-971997-9819981999-2000
Interest (in lakes of rupees)2025151830
Draw the bar graph to represent the above information.

Given table shows
the interest paid by a company(in lakhs)
Year                           $$1995-96$$            $$1996-97$$           $$1997-98$$        $$1998-1999$$               $$1999-2000$$
Interest(in lakhs)             $$20$$                       $$25$$                          $$15$$                           $$18$$                            $$30$$

1475693_1675544_ans_a960400b36904bbaac0799ae9668c1fc.png


Class 8 Maths Extra Questions