CBSE Questions for Class 12 Commerce Applied Mathematics Standard Probability Distributions Quiz 11 - MCQExams.com

The odds in favour of India winning any cricket match is $$2 : 3$$. What is the probability that if India plays $$5$$ matches, it wins exactly $$3$$ of them?
  • $$^5C_3\left(\dfrac{2}{5}\right)^2\left(\dfrac{3}{5}\right)^3$$
  • $$^5C_3\left(\dfrac{2}{3}\right)^2\left(\dfrac{1}{3}\right)^3$$
  • $$^5C_3\left(\dfrac{2}{5}\right)^3\left(\dfrac{3}{5}\right)^2$$
  • $$^5C_3\left(\dfrac{2}{3}\right)^2\left(\dfrac{1}{3}\right)^2$$
Suppose a machine produces metal parts that contain some defective parts with probability $$0.05$$. How many parts should be produced in order that the probability of atleast one part being defective is $$\dfrac 12$$ or more? 
(Given that, $$\log_{10}95=1.977$$ and $$\log_{10}2=0.3$$) 
  • $$11$$
  • $$12$$
  • $$15$$
  • $$14$$
Each of the $$n$$ passengers sitting in a bus may get down from it at the next stop with probability $$p$$. Moreover, at the next stop either no passenger or exactly one passenger boards the bus. The probability of no passenger boarding the bus at the next stop being $$p_o$$. Find the probability that when the bus continues on its way after the stop, there will again be n passengers in the bus
  • $$(1 - p)^{n-1}. [ p_o (1- p) + np(1 -p_0 )]$$
  • $$1- (1 - p)^{n-1}. [ p_o (1- p) + np(1 -p_0 )]$$
  • $$p^{n}. [ p_o (1- p) + np(1 -p_0 )]$$
  • $$1 -p^{n}. [ p_o (1- p) + np(1 -p_0 )]$$
An experiment succeeds twice as often as it fails. The probability of at least $$1$$ successes in the six trials of this experiment is:
  • $$\dfrac {496}{729}$$
  • $$\dfrac {192}{729}$$
  • $$\dfrac {240}{729}$$
  • $$\dfrac {256}{729}$$
If $$X$$ is a poisson variate and $$P(X = 1) = 2P(X = 2)$$, then $$P(X = 3) = X$$
  • $$\displaystyle\frac{e^{-1}}{6}$$
  • $$\displaystyle\frac{e^{-2}}{2}$$
  • $$\displaystyle\frac{e^{-1}}{2}$$
  • $$\displaystyle\frac{e^{-1}}{3}$$
The scores on standardized admissions test are normally distributed with a mean of $$500$$ and a standard deviation of $$100$$. What is the probability that a randomly selected student will score between $$400$$ and $$600$$ on the test?
  • About $$63\%$$
  • About $$65\%$$
  • About $$68\%$$
  • About $$70\%$$
Alice, Bob and Carol repeatedly take turns tossing a die. Alice begins; Bob always follows Alice, Carol always follows Bob, and Alice always follows Carol. Find the probability that Carol will be the first one to toss a six. (The probability of obtaining a six on any toss is 1/6, independent of the outcome of any other toss.)
  • $$\dfrac{1}{3}$$
  • $$\dfrac{2}{9}$$
  • $$\dfrac{5}{18}$$
  • $$\dfrac{25}{91}$$
If it rains on Republic Day parade an Auto Riksha earns Rs. $$240,$$ on the other hand it does not rain he loses Rs. $$60$$. The probability of rain on Republic Day parade is $$0.6$$. What is the value of expected income of an Auto Riksha on Republic Day parade?
  • Rs. $$150$$
  • Rs. $$45$$
  • Rs. $$120$$
  • Rs. $$10$$
The average length of time required to complete a jury questionnaire is $$40$$ minutes, with a standard deviation of $$5$$ minutes. What is the probability that it will take a prospective juror between $$30$$ and $$50$$ minutes to complete the questionnaire?
  • About $$85\%$$
  • About $$90\%$$
  • About $$95\%$$
  • none
The average length of time required to complete a jury questionnaire is $$40$$ minutes, with a standard deviation of $$5$$ minutes. What is the probability that it will take a prospective juror between $$35$$ and $$45$$ minutes to complete the questionnaire?
  • About $$68\%$$
  • About $$72\%$$
  • About $$76\%$$
  • About $$84\%$$
The marks secured by $$400$$ students in a Mathematics test were normally distributed with mean $$65$$. If $$120$$ students got marks above $$85$$, the number of students securing marks between $$45$$ and $$65$$ is
  • $$120$$
  • $$20$$
  • $$80$$
  • $$160$$
If $${ \mu  }_{ 2 }=20,{ \mu  }_{ 2 }^{ 1 }=276$$ for a discrete random variable $$X$$, then the mean of the random variable $$X$$ is
  • $$16$$
  • $$5$$
  • $$2$$
  • $$1$$
The length of similar components produced by a company is approximated by a normal distribution model with a mean of $$5$$ cm and a standard deviation of $$0.02$$ cm. If a component is chosen at random, what is the probability that the length of this component is between $$4.96$$ and $$5.04$$ cm?
  • $$0.9544$$
  • $$0.1236$$
  • $$0.7265$$
  • $$0.9546$$
The probability that Dhoni will hit century in every ODI matches he plays is $$\dfrac{1}{5}$$. When he plays $$6$$ matches in World Cup 2011, the probability that he will score at least one century is:
  • $$\dfrac{2357}{3125}$$
  • $$\dfrac{121}{3125}$$
  • $$\dfrac{768}{3125}$$
  • $$\dfrac{4096}{15625}$$
If $$x$$ follows a binomial distribution with parameters $$n=100$$ and $$p=\dfrac{1}{3}$$, then $$P(x-r)$$ is maximum, when $$r$$ equals 
  • $$16$$
  • $$32$$
  • $$33$$
  • None of these
The annual salaries of employees in a large company are approximately normally distributed with a mean of $$50,000$$ and a standard deviation of $$20,000$$.  What percent of people earn between $$45,000$$ and $$65,000$$?
  • $$56.23$$%
  • $$47.4$$%
  • $$37.2$$%
  • $$38.56$$%
The mean of a binomial distribution is $$5$$ and its standard deviation is $$2$$. Then the values of $$n$$ and $$p$$ are:
  • $$\left( \cfrac { 4 }{ 5 } ,25 \right) $$
  • $$\left( 25,\cfrac { 4 }{ 5 } \right) $$
  • $$\left( \cfrac { 1 }{ 5 } ,25 \right) $$
  • $$\left( 25,\cfrac { 1 }{ 5 } \right) $$
Let X denotes the number of times head occur in n tosses of a fair coin. If $$P(X = 4), P(X = 5)$$ and $$P(X = 6)$$ are in AP, then the value of n is
  • 7, 14
  • 10, 14
  • 12, 7
  • 14, 12
Three six faced dice are thrown together. The probability that the sum of the numbers appearing on the dice is $$k\left( 3\le k\le 8 \right) $$ is
  • $$\cfrac { { k }^{ 2 } }{ 432 } $$
  • $$\cfrac { k(k-1) }{ 432 } $$
  • $$\cfrac { (k-1)(k-2) }{ 432 } $$
  • $$\cfrac { k(k-1)(k-2) }{ 432 } $$
The probability that Dhoni will hit century in every ODI matches he lays is $$\dfrac{1}{5}$$. If he plays $$6$$ matches in World Cup 2011, the probability that he will score century in all the $$6$$ test matches is:
  • $$\dfrac{1}{3125}$$
  • $$\dfrac{5}{3125}$$
  • $$\dfrac{4096}{15625}$$
  • $$\dfrac{1555}{3125}$$
The value of $$\frac{C_0}{1.3}$$ - $$\frac{C_1}{2.3} $$+ $$\frac{C_2}{3.3} $$- $$\frac{C_3}{4.3}$$+ ..................+$$ (-1)^n$$ $$\frac{C_n}{(n + 1)}$$$$\cdot3$$ 
  • $$\dfrac{3}{n+1}$$
  • $$\dfrac{n+3}{3}$$
  • $$\dfrac{1}{3(n+1)}$$
  • None of these
A throws a coin $$4$$ times. If he get a head all four times, he is to get a reward of Rs. $$240$$, on the other hand if he does not get head he is to loose Rs. $$24$$. He is expected to win
  • Rs. $$50$$ Profit
  • Rs. $$10$$ Profit
  • Rs.$$25$$ Loss
  • Rs. $$7.5$$ Loss
There are four EVMs in a polling centre. It is known that two of them are fixed. They are tested  one by one in a random orders till both the faulty EVMs are identified. The probability that only two tests are needed to identify such machines is---
  • $$\dfrac {1}{6}$$
  • $$\dfrac {1}{9}$$
  • $$\dfrac {4}{9}$$
  • $$\dfrac {1}{3}$$
There is a probability that 4 out of 10 students appearing in CA CPT exams will qualify for CA course after passing CA CPT exam, the probability that of 5 students none will join CA course is.......
  • $$0.01$$
  • $$0.065$$
  • $$0.43$$
  • $$40.08$$
There is a probability that 4 out of 10 students appearing in CA CPT exams will qualify for CA course after CA CPT exam. The probability that at least of the five students will join CA course is.......
  • $$0.92$$
  • $$0.66$$
  • $$0.45$$
  • $$0.08$$
The probability that Sania wims Wimbledon tournaments final is $$\dfrac{1}{3}$$. If Sania Mirza plays $$3$$ round of Wimbledon final, the probability that she wins at least one round of match is:
  • $$\dfrac{8}{27}$$
  • $$\dfrac{19}{27}$$
  • $$\dfrac{10}{27}$$
  • $$\dfrac{17}{27}$$
The probability of an even happens in one trial of an experiment is $$0.3$$. Three independent trials of the experiments are performed. Find the probability that the event A happens at least once.
  • $$0.657$$
  • $$0.965$$
  • $$0.796$$
  • $$0.509$$
If X and Y are independent binomial variates $$B\left(5, \dfrac{1}{2}\right)$$ and $$B\left(7, \dfrac{1}{2}\right)$$, then $$P(X+Y=3)$$, is?
  • $$\dfrac{35}{47}$$
  • $$\dfrac{55}{1024}$$
  • $$\dfrac{220}{512}$$
  • $$\dfrac{11}{204}$$
If $$3%$$ of electric bulbs manufactured by a company are defective; the probability that in a sample of $$100$$ bulbs exactly five are defective is
  • $$\dfrac{e^{-0.03}(0.03)^5}{ 5!}$$
  • $$\dfrac{e^{-0.3}0.03^5}{ 5!}$$
  • $$\dfrac{e^{-3}0.03^5}{ 5!}$$
  • $$\dfrac{e^{-0.3}3^{-5}}{ 5!}$$
The mean and variance of a random variable $$X$$ having a binomial distribution are $$4$$ and $$2$$ respectively then $$P(X = 1)$$ is ______
  • $$\dfrac{1}{16}$$
  • $$\dfrac{1}{8}$$
  • $$\dfrac{1}{4}$$
  • $$\dfrac{1}{32}$$
In a Binomial distribution, the mean is three times its variance. What is the probability of exactly $$3$$ successes out of $$5$$ trials?
  • $$\dfrac{80}{243}$$
  • $$\dfrac{40}{243}$$
  • $$\dfrac{20}{243}$$
  • $$\dfrac{10}{243}$$
If X follows the binomial distribution with parameters $$n=6$$ and $$p$$ and $$9P\left( {X = 4} \right) = P\left( {X = 2} \right)$$ then $$p$$ is:
  • $$1/4$$
  • $$1/3$$
  • $$1/2$$
  • $$2/3$$
If the range of a random variable $$X$$ is $$0,1,2,3,......$$ with $$P(X=k)=\dfrac {(k+1)a}{3^{k}}$$ for $$k \ge 0$$, then $$a=$$
  • $$2/3$$
  • $$4/9$$
  • $$8/27$$
  • $$16/81$$
Suppose $$X$$ follows binomial distribution with parameters $$n=100$$ and $$p=\frac{1}{3}$$ then $$P(x=r)$$ is maximum when $$r=$$  
  • $$49$$
  • $$50$$
  • $$12$$
  • $$33$$
If x is a poisson variable such that $$P(X = 2) = \dfrac{2}{3}P(X = 1)$$ then p (x = 3) is
  • $$e^{\dfrac{-4}{3}}$$
  • $$\dfrac{64}{162}e^{\dfrac{-4}{3}}$$
  • $$e^{\dfrac{-3}{4}}$$
  • $$e^{\dfrac{3}{4}}$$
If X is a random poisson variate such that $$E(X^2)=6$$, then $$E(x)=$$?
  • $$3$$
  • $$2$$
  • $$-3$$ & $$2$$
  • $$-2$$
If the number of telephone calls an operator receives between $$10:00$$ pm to $$10:10$$ pm following poisson distribution with mean $$3$$. The probability that the operator receives one call during that interval the next day is
  • $$\dfrac{1}{e}$$
  • $$\dfrac{3}{e^{3}}$$
  • $$\dfrac{3}{e^{-2}}$$
  • None of these
For a binomial distribution $$\bar x = 4$$, $$\sigma^ 2 = 3$$ then the distribution of $$x$$ is
  • $${\left( {\frac{1}{4} + \frac{3}{4}} \right)^{15}}$$
  • $${\left( {\frac{3}{4} + \frac{1}{4}} \right)^{16}}$$
  • $${\left( {\frac{1}{2} + \frac{1}{4}} \right)^{16}}$$
  • $${\left( {\frac{1}{2} + \frac{1}{4}} \right)^{8}}$$
For a binomial distribution mean is $$6$$ and $$S.D$$ is $$\sqrt{2}$$. The distribution is
  • $$\left(\dfrac{2}{3}+\dfrac{1}{3}\right)^9$$
  • $$\left(\dfrac{1}{3}+\dfrac{2}{3}\right)^9$$
  • $$\left(\dfrac{1}{5}+\dfrac{4}{5}\right)^9$$
  • $$\left(\dfrac{4}{5}+\dfrac{1}{5}\right)^9$$
There are $$4$$ defective items in a lot of $$15$$ items. The items are selected one by one at random without replacement till the last defective item is drawn. The probability that the 10th item examined is the last defective item is 
  • $$\dfrac{1}{{65}}$$
  • $$\dfrac{2}{{65}}$$
  • $$\dfrac{3}{{65}}$$
  • $$\dfrac{4}{{65}}$$
It is observed that $$25\%$$ of the cases related to child labour reported to the police station are solved. If $$6$$ new cases are reported, then the probability that atleast $$5$$ of them will be solved is?
  • $$\left(\dfrac{1}{6}\right)^6$$
  • $$\dfrac{19}{1024}$$
  • $$\dfrac{19}{2048}$$
  • $$\dfrac{19}{4096}$$
If variable $$x$$ takes values $$0,1,2......,n$$ with frequencies proportional to binomial coefficients $$n_{c_{0}},n_{c_{1}},n_{c_{2}}.....,n_{c_{n}}$$. Then the variance of $$x$$ is....
  • $$\cfrac{n}{4}$$
  • $$\cfrac{n^2-1}{12}$$
  • $$\cfrac{n}{2}$$
  • $$\cfrac{n}{3}$$
Consider two events A and B in a sample space such that P(A)=0.3 and P(B)=0.Is it possible that the two events are disjoint?
  • Yes
  • No
  • May be
  • Incomplete data
If $$X$$ has a binomial distribution, $$B\left(n,p\right)$$ with parameters $$n$$ and $$p$$ such that $$P\left(X-2\right)=P\left(X=3\right)$$, then $$E\left(X\right)$$, the mean of variable $$X$$, is
  • $$2-p$$
  • $$3-p$$
  • $$p/2$$
  • $$p/3$$
There are twenty bags each containing 10 bulbs and it is knows that no bag contains more than 5 defective bulbs and 3 bags have 5 defective bulbs. 4 bags have atleast 4 defective bulbs, 5 bags have atleast 3 defective bulbs, 6 bags have atleast 2 defective bulbs and 7 bags have atleast 1 defective bulb. Then the ratio of total defective bulbs is to non-defective bulbs is
  • $$\dfrac { 4 }{ 7 } $$
  • $$\dfrac { 3 }{ 7 } $$
  • $$\dfrac { 2 }{ 7 } $$
  • $$\dfrac { 1 }{ 7 } $$
In a poisson distribution if $$P(X=2)=P(X=3)$$ then, the value of its parameter $$\lambda$$ is:
  • $$3$$
  • $$0$$
  • $$6$$
  • $$2$$
Eight coins are tossed at a time, the probability of getting atleast $$6$$ heads up, is
  • $$\dfrac {7}{64}$$
  • $$\dfrac {57}{64}$$
  • $$\dfrac {37}{256}$$
  • $$\dfrac {229}{256}$$
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