Algebra

Probability

Easy

applied

The mean of the number of heads in a simultaneous toss of three coins is

$\frac{2}{3}$

$\frac{3}{4}$

$\frac{1}{3}$

$\frac{3}{2}$

✅ Correct Option: 4

The number of heads follows a binomial distribution with $n=3$ and $p=\frac{1}{2}$ .

Mean $= np = 3\times\frac{1}{2} = \frac{3}{2}$ .

2025: 29 May Shift 2

Match List-I with List-II

If the random variable x has the following distribution:

x	0	1	2	otherwise
P(x)	k	k	2k	0

Choose the correct answer from the options given below:

2025: 22 May Shift 2

For a Binomial distribution, B(n,p), where p+q=1, the sum and product of mean and variance are 8 and 12 respectively, when the value of n is:

2023: 22 May Shift 3

For the following probability distribution :

X	1	2	3	4
P(X)	1/10	1/5	3/10	2/5

$E(X^2)$ is equal to :

2023: 15 June Shift 2

If in a binomial distribution $n = 4$ , $P(X=0) = \frac{16}{81}$ , then $P(X=4)$ equals :

2026: 22 May Shift 2

A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is:

2022: 23 Aug Shift 1

Consider an experiment of tossing 3 coins simultaneously. Define the following events:

$E$ = [Three heads or three tails appear]

$F$ = [At least two heads appear] and

$G$ = [At most two heads appear]

Choose the correct option:

Solution