Question

Find the probability distribution of number of tails in the simultaneous tosses of three coins.

Answer 1

When three coins are tossed simultaneously, the sample space is

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Let X represent the number of tails.

It can be seen that X can take the value of 0, 1, 2 or 3

P(X = 0) = P(HHH) = `1/8`

P(X = 1) = P(HHT) + P(HTH) + P(THH) =`1/8 +1/8+1/8 =3/8`

P(X = 2) = P(HTT) + P(THT) + P(TTH) =`1/8+1/8+1/8 = 3/8`

P(X = 3) = P(TTT) = `1/8`

Thus, the probability distribution is as follows.

X	0	1	2	3
P(X)	`1/8`	`3/8`	`3/8`	`1/8`