Question

Find the probability distribution of number of heads in four tosses of a coin

Answer 1

Let X denote the number of heads.

Sample space of the experiment is

S = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, TTHH, THTH, HTHT, THHT, HTTT, THTT, TTHT, TTTH, TTTT}

The values of X corresponding to these outcomes are as follows.

X(TTTT) = 0

X(HTTT) = X(THTT) = X(TTHT) = X(TTTH) = 1

X(HHTT) = X(HTTH) = X(TTHH) = X(THTH) = X(HTHT) = X(THHT) = 2

X(HHHT) = X(HHTH) = X(HTHH) = X(THHH) = 3

X(HHHH) = 4

∴ X is a discrete random variable that can take values 0, 1, 2, 3, 4.

The probability distribution of X is then obtained as follows:

X	0	1	2	3	4
P(X = x)	`(1)/(16)`	`(4)/(16)`	`(6)/(16)`	`(4)/(16)`	`(1)/(16)`