CBSE Questions for Class 12 Commerce Applied Mathematics Standard Probability Distributions Quiz 7 - MCQExams.com

An experiment succeeds twice as often as it fails. Find the chance that in the next six trials, there shall be at least four successes.
  • $$\displaystyle \frac{233}{729}$$
  • $$\displaystyle \frac{64}{729}$$
  • $$\displaystyle \frac{496}{729}$$
  • $$\displaystyle \frac{432}{729}$$
$$8$$ coins are tossed simultaneously. The probability of getting at least 6 heads is
  • $$57/64$$
  • $$229/256$$
  • $$7/64$$
  • $$37/256$$
The probability that a marksman will hit a target is given as 1/Then his probability at least one hit in 10 shots is.
  • $$\displaystyle 1-\left ( \frac{4}{5}\right)^{10}$$
  • $$\displaystyle \frac{1}{5}$$
  • $$\displaystyle 1-\frac{1}{5},$$
  • none of these.
A fair coin is tossed n times. if the probability that head occurs $$6$$ times is equal to the probability that head occurs $$8$$ times, then value of $$n$$ is
  • $$24$$
  • $$48$$
  • $$14$$
  • $$16$$
If $$X$$ and $$Y$$ are independent binomial variate $$B (5, 1/2)$$ and $$B (7, 1/2)$$, then $$P(X+Y=3)$$ is
  • $$55/1024$$
  • $$55/4098$$
  • $$55/2048$$
  • None of these
A random variable X follows binomial distribution with mean a and variance b. Then
  • $$a > b > 0$$
  • $$\dfrac {a}{b} > 1$$
  • $$\dfrac {a^2}{a-b}$$ is an integer
  • $$\dfrac {a^2}{a+b}$$ is an integer
In a hurdle race, a runner has probability $$p$$ of jumping over a specific hurdle. Given that in $$5$$ trials, the runner succeeded $$3$$ times, the conditional probability that the runner had succeeded in the first trail is 
  • $$\displaystyle\frac { 3 }{ 5 } $$
  • $$\displaystyle\frac { 2 }{ 5 } $$
  • $$\displaystyle\frac { 1 }{ 5 } $$
  • $$\displaystyle\frac { 4 }{ 5 } $$
A fair die is tossed eight times. Probability that on the eighth throw a third six is observed is
  • $$\displaystyle^{ 8 }{ { C }_{ 3 } }\frac { { 5 }^{ 8 } }{ { 6 }^{ 8 } } $$
  • $$\displaystyle^{ 7 }{ { C }_{ 2 } }\frac { { 5 }^{ 5 } }{ { 6 }^{ 8 } } $$
  • $$\displaystyle^{ 7 }{ { C }_{ 2 } }\frac { { 5 }^{ 5 } }{ { 6 }^{ 7 } } $$
  • None of these
Suppose $$X~B(n, p)$$ and $$P(X=3)=P(X=5)$$. If $$p > \dfrac 12$$, then
  • $$n\leq 7$$
  • $$n > 8$$
  • $$n\geq 9$$
  • none of these
$$15$$ coins are tossed, then the probability of getting $$10$$ heads will be
  • $$\dfrac {511}{32768}$$
  • $$\dfrac {1001}{32768}$$
  • $$\dfrac {3003}{32768}$$
  • $$\dfrac {3005}{32768}$$
A bag contains three tickets numbered $$1, 2$$ and $$3$$. A ticket is drawn at random and put back in the bag, and this is done four times. The probability that the sum of the numbers drawn is even is
  • $$\dfrac {40}{81}$$
  • $$\dfrac {41}{81}$$
  • $$\dfrac {14}{27}$$
  • $$\dfrac {13}{81}$$
If X follows a binomial distribution with parameters $$n=100$$ and $$p=1/3$$, find r for which $$P(X=r)$$ is maximum
  • $$33$$
  • $$22$$
  • $$11$$
  • $$15$$
The probability that $$X=3$$ equals
  • $$\displaystyle \frac {25}{216}$$
  • $$\displaystyle \frac {25}{36}$$
  • $$\displaystyle \frac {5}{36}$$
  • $$\displaystyle \frac {125}{216}$$
The probability that a marksman will hit a target is given as $$\displaystyle \frac{1}{5}$$ ,then his probability of at least one hit in 10 shots is 
  • $$\displaystyle 1-\left ( \frac{4}{5} \right )^{10}$$
  • $$\displaystyle \frac{1}{5^{10}}$$
  • $$\displaystyle 1-\frac{1}{5^{10}}$$
  • None of these
If the mean of a binomial distribution is $$25$$, then find the interval in which the standard deviation lies.
  • $$[0,5)$$
  • $$(0,5]$$
  • $$[0,25)$$
  • $$(0,25]$$
Find the probability of getting $$4$$ exactly thrice in $$7$$ throws of a die
  • $$^7C_3\left (\dfrac {1}{6}\right )^3\left (\dfrac {5}{6}\right )^4$$
  • $$^7C_4\left (\dfrac {1}{6}\right )^4\left (\dfrac {5}{6}\right )^3$$
  • $$^7C_4\left (\dfrac {1}{6}\right )^3\left (\dfrac {5}{6}\right )^4$$
  • $$^7C_3\left (\dfrac {1}{6}\right )^4\left (\dfrac {5}{6}\right )^3$$
Numbers are selected at random, one at a time, from the two digit numbers $$00, 01, 02,....., 99$$ with replacement. An event $$E$$ occurs if & only if the product of the two digits of a selected number is $$18.$$ If four numbers are selected, find the probability that the event $$E$$ occurs at least $$3$$ times.
  • $$\dfrac{97}{25^4}$$
  • $$\dfrac{1}{25^4}$$
  • $$\dfrac{95}{25^4}$$
  • $$\dfrac{90}{25^4}$$
Suppose $$X$$ follows a binomial distribution with parameters $$n$$ and $$p$$, where $$0<p<1$$. If $$\displaystyle \frac { P\left( X=r \right)  }{ P\left( X=n-r \right)  } $$ is independent of $$n$$ and $$r$$, then
  • $$\displaystyle p=\frac { 1 }{ 2 } $$
  • $$\displaystyle p=\frac { 1 }{ 3 } $$
  • $$\displaystyle p=\frac { 1 }{ 4 } $$
  • None of these
If $$n$$ distinct objects are distributed randomly into $$n$$ distinct boxed
  • then the probability that no box is empty is $$\displaystyle \frac{n!}{n^{n}}$$
  • then the probability that exactly one box is empty is $$\displaystyle \frac{n!^{n}C_{2}}{n^{n}}$$
  • then the probability that a particular box get exactly $$r$$ objects is $$\displaystyle \frac{^{n}C_{r}(n-1)^{n-r}}{n^{n}}$$
  • None of these
Anand plays with Karpov $$3$$ games of chess. The probability that he wins a game is $$0.5$$, looses with probability $$0.3$$ and ties with probability $$0.2$$. If he plays $$3$$ games then find the probability that he wins atleast two games
  • $$1/2$$
  • $$1/3$$
  • $$1/4$$
  • $$1/5$$
A fair die is rolled $$(2n+1)$$ times. The probability that the faces with even number show odd number of times is
  • $$\displaystyle \frac {3n+1}{4n+2}$$
  • $$\displaystyle \frac {3}{4}$$
  • $$\displaystyle \frac {2}{3}$$
  • $$\displaystyle \frac {1}{2}$$
The value of P(2) in a Binomial distribution when $$\displaystyle P=\frac{1}{6}$$ and n = 5 is 
  • $$\displaystyle \dfrac{3125}{7776}$$
  • $$\displaystyle \dfrac{250}{7776}$$
  • $$\displaystyle \dfrac{1250}{7776}$$
  • $$\displaystyle \dfrac{25}{7776}$$
A fair coin is tossed at a fixed number of times. If the probability of getting exactly $$3$$ heads equals the probability of getting exactly $$5$$ heads, then the probability of getting exactly one head is 
  • $$\dfrac{1}{64}$$
  • $$\dfrac{1}{32}$$
  • $$\dfrac{1}{16}$$
  • $$\dfrac{1}{8}$$
The mean number of heads in three tosses of a coin is 
  • $$\displaystyle \frac{5}{2}$$
  • $$\displaystyle \frac{1}{2}$$
  • $$\displaystyle \frac{3}{2}$$
  • $$\displaystyle \frac{1}{8}$$
Given $$\displaystyle X\sim N\left( 10,36 \right) $$  what is the variance of X?
  • $$10$$
  • $$\displaystyle \sqrt { 10 } $$
  • $$36$$
  • $$6$$
What is the possibility of getting at least 6 heads if eight coins are tossed simultaneously?
  • $$\dfrac{37}{256}$$
  • $$\dfrac{25}{57}$$
  • $$\dfrac{1}{13}$$
  • $$\dfrac{5}{27}$$
The probability that an event does not happen in one trial is $$0.8$$. The probability that the event happens atmost once in three trials is
  • $$0.896$$
  • $$0.791$$
  • $$0.642$$
  • $$0.592$$
Suppose $$X$$ follows a binomial distribution with parameters $$n$$ and $$p$$, where $$0 < p <1   ,\dfrac {P(X = r)}{P(X = n - r)}$$ is independent of $$n$$ for every $$r$$, then $$p =$$
  • $$\dfrac {1}{2}$$
  • $$\dfrac {1}{3}$$
  • $$\dfrac {1}{4}$$
  • $$\dfrac {1}{8}$$
Given $$\displaystyle X\sim B\left( n,p \right) $$
If $$\displaystyle E\left( X \right) =6,var\left( X \right) =4.2$$ then what is the number of trials?
  • $$21$$
  • $$10$$
  • $$20$$
  • $$7$$
If $$X$$ is a poisson variate such that $$\alpha =P(X = 1) = P (X = 2)$$ then $$P (X = 4) =$$
  • $$2\alpha$$
  • $$\dfrac {\alpha}{3}$$
  • $$\alpha e^{-2}$$
  • $$\alpha e^{2}$$
Two persons A and B are throwing an unbiased six faced die alternatively, with the condition that the person who throws $$3$$ first wins the game. If A starts the game, the probabilities of A and B to win the same are respectively
  • $$\dfrac {6}{11}, \dfrac {5}{11}$$
  • $$\dfrac {5}{11}, \dfrac {6}{11}$$
  • $$\dfrac {8}{11}, \dfrac {3}{11}$$
  • $$\dfrac {3}{11}, \dfrac {8}{11}$$
If $$x$$ follows the Binomial distribution with parameters $$n=6$$ and  $$p$$ and $$9P(X=4) = P(X=2)$$, then $$p$$ is 
  • $$\dfrac {1}{4}$$
  • $$\dfrac {1}{3}$$
  • $$\dfrac {1}{2}$$
  • $$\dfrac {2}{3}$$
The probability that an individual suffers a bad reaction from an in injection is $$0.001$$. The probability that out of $$2000$$ individuals exactly three will suffer bad reaction is 
  • $$\dfrac{2}{e^2}$$
  • $$\dfrac{2}{5e^2}$$
  • $$\dfrac{8}{5e^2}$$
  • $$\dfrac{4}{3e^3}$$
The number of times a fair coin must be tossed so that the probability of getting at least one head is $$0.8$$ is-
  • $$7$$
  • $$6$$
  • $$5$$
  • $$3$$
A die is thrown a fixed number of times. If probability of getting even number $$3$$ times is same as the probability of getting even number $$4$$ times, then probability of getting even number exactly once is
  • $$\dfrac{1}{4}$$
  • $$\dfrac{3}{128}$$
  • $$\dfrac{5}{64}$$
  • $$\dfrac{7}{128}$$
A fair coin is tossed $$99$$ times. Let X be the number of times heads occurs. Then $$P(X=r)$$ is maximum when r is
  • $$49$$
  • $$52$$
  • $$51$$
  • None of these
Out of $$800$$ families with $$4$$ children each, the expected percentage of families having almost $$2$$ girls, is:
  • $$68.75 \%$$
  • $$69.25 \%$$
  • $$62.50 \%$$
  • None of these
For a poisson distribution with parameter $$\lambda = 0.25$$, the value of the $$2^{nd}$$ moment about the origin is
  • $$0.25$$
  • $$0.3125$$
  • $$0.0625$$
  • $$0.025$$
If the mean and standard deviation of a binomial distribution are $$12$$ and $$2$$ respectively, then the value of its parameter $$p$$ is
  • $$\cfrac{1}{2}$$
  • $$\cfrac{1}{3}$$
  • $$\cfrac{2}{3}$$
  • $$\cfrac{1}{4}$$
The mean and the variance in a binomial distribution are found to be $$2$$ and $$1$$ respectively. The probability $$P(X = 0)$$ is
  • $$\dfrac{1}{2}$$
  • $$\dfrac{1}{4}$$
  • $$\dfrac{1}{8}$$
  • $$\dfrac{1}{16}$$
In a Poisson distribution if $$P\left( X=2 \right) =P\left( X=3 \right) $$ then the value of its parameter $$\lambda $$ is
  • $$6$$
  • $$2$$
  • $$3$$
  • $$0$$
If $$X$$ is a Poisson's variate such that $$P(X=1)=3P(X=2)$$, then find the variance of $$X$$.
  • $$\cfrac 38$$
  • $$\cfrac 13$$
  • $$\cfrac 23$$
  • $$\cfrac 54$$
If mean and variance of a Binomial variable X are 2 and 1 respectively, then the probability that X takes a value greater than 1 is
  • $$\dfrac{2}{3}$$
  • $$\dfrac{4}{5}$$
  • $$\dfrac{7}{8}$$
  • $$\dfrac{11}{16}$$
If the mean and variance of a binomial distribution are $$4$$ and $$2$$, respectively. Then, the probability of atleast $$7$$ successes is
  • $$\dfrac {3}{214}$$
  • $$\dfrac {4}{173}$$
  • $$\dfrac {9}{256}$$
  • $$\dfrac {7}{231}$$
A box contains $$15$$ green and $$10$$ yellow balls. If $$10$$ balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is
  • $$\displaystyle\frac{12}{5}$$
  • $$6$$
  • $$4$$
  • $$\displaystyle\frac{6}{25}$$
Which of the following are correct regarding normal distribution curve?
(i) Symmetrical about the line $$X=\mu $$ (Mean)
(ii) Mean $$=$$ Median $$=$$ Mode
(iii) Unimodal
(iv) Points of inflexion are at $$X=\mu \pm \sigma $$
  • (i), (ii)
  • (ii), (iv)
  • (i), (ii), (iii)
  • All of these
The probability that a student get success in a competition is $$\dfrac { 3 }{ 4 }$$. The probability that exactly $$2$$ out of $$4$$ students get success, is
  • $$\dfrac { 9 }{ 41 } $$
  • $$\dfrac { 25 }{ 128 } $$
  • $$\dfrac { 1 }{ 5 } $$
  • $$\dfrac { 27 }{ 128 } $$
The mode of the binomial distribution for which mean and standard deviation are $$10$$ and $$\sqrt { 5 } $$ respectively, is
  • $$7$$
  • $$8$$
  • $$9$$
  • $$10$$
If r.v. $$ X\sim B\left( n=5,P=\cfrac { 1 }{ 3 }  \right)$$, then $$P(2< X< 4)=$$...........
  • $$\cfrac { 80 }{ 243 } $$
  • $$\cfrac { 40 }{ 243 } $$
  • $$\cfrac { 40 }{ 343 } $$
  • $$\cfrac { 80 }{ 343 } $$
The probability that an event does not happen in one trial is 0.8.The probability that the event happens atmost once in three trails is 
  • 0.896
  • 0.791
  • 0.642
  • 0.592
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers