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 $\small X+Y\geq 1$.