MCQ's on Binomial Distribution | Stat Wiki

 

MCQs on Binomial Distribution

1. Ten coins are thrown simultaneously. Find the probability of getting atleast seven heads.

a) $\small \frac{170}{1024}$    b) $\small \frac{176}{1024}$   c) $\small \frac{169}{1089}$  d)$\small \frac{144}{1225}$

 

 Ans. b) $\small \frac{176}{1024}$

 

2. A and B play a game in which their chances of winning are in the ratio 3:2. Find A's chances of winning at least three games out of the five games played.

a) 0.66  b) 0.78  c)0.68  d) 0.64

Ans: c) 0.68

Read More: MCQs on mgf law of large numbers

3. The mean and variance of the binomial distribution are 4 and $\small \frac{4}{3}$ respectively. Find $\small P(X\geq 1)$.

a) 0.99863  b) 0.89762  c) 0.9756  d) 0.88745

Ans: a) 0.99863

4.We are given $\small X \sim B(3,\frac{1}{3}) \thinspace and \thinspace  Y \sim B(5, \frac{1}{3})$. then $\small X+Y$ follows what?

a) $\small 8, \frac{1}{3}$  b) $\small 8, \frac{2}{3}$  c) $\small 3, \frac{1}{3}$  d) $\small 5, \frac{1}{3}$

Ans: 

5. In a binomial distribution consisting of 5 independent trails, probabilities of 1 and 2 successes are 0.4096 and 0.2048 respectively. Find the parameter p of the distribution.

a) 0.3  b) 0.1  c) 0.2 d) 0.4

Ans. c) 0.2

6. With the usual notations, find p for a binomial random variable X if n = 6 and if $\small 9P(X=4)=P(X=2)$.

a) 0.20 b) 0.35 c) 0.45 d) 0.25

Ans: d) 0.25

Read Also: MCQ's on random variables and distribution functions

7. $X$ is a random variable following binomial distribution with, mean 2.4 and variance 1.44. Find $\small P(X\geq 5), P(1< X\leq 4)$.

Ans. Do it Yourself. (If you face any problem to solve this, drop a message in our facebook page.)

8. A card is drawn and replaced in an ordinary deck of 52 cards. How many times must a card be drawn so that (i) there is at least an even chance of drawing a heart, (ii) the probability of drawing a heart is greater than 3/4 ?

 

a) 3, 5 b) 2, 5 c) 4,6 d) 3, 6

Ans: a) 3, 5

 

Do it yourself

 

1. $X$ is a random variable following binomial distribution with, mean 2.4 and variance 1.44. Find $\small P(X\geq 5), P(1< X\leq 4)$.

Ans. Do it Yourself. (If you face any problem to solve this, drop a message in our facebook page.)

 

 

2. X is binomially distributed with parameters n and p. What is the distribution of $\small Y=n-X$ ? [Delhi Univ. B.Sc. (Math Hons.)]

Do it Yourself.👍

 

3. If the independent random variables $\small X, Y$ are binomially distributed, respectively with n = 3, $\small p=\frac{1}{3}$, write down the probability that $\small X+Y\geq 1$.