Question

Find the probability distribution of number of heads in two tosses of a coin.

If two coins are tossed simultaneously, write the probability distribution of the number of heads.

Answer 1

When one coin is tossed twice, the sample space is

{HH, HT, TH, TT}

Let X represent the number of heads s in two tosses of a coin.

∴ X(HH) = 2,

X(HT) = 1,

X(TH) = 1,

X(TT) = 0

Therefore, X can take the value of 0, 1 or 2.

It is known that,

P(HH) = P(HT) = P(TH) = P(TT) = `1/4`

P(X = 0) = P(TT) = `1/4`

P(X = 1) = P(HT) + P(TH) = `1/4 +1/4 = 1/2`

P(X = 2) = P(HH) = `1/4`

Thus, the required probability distribution is as follows:

X	0	1	2
P(X)	`1/4`	`1/2`	`1/4`