Question

Three fair coins are tossed simultaneously. If X denotes the number of heads, find the probability distribution of X. 

Answer 1

Three fair coins are tossed simultaneously.

∴ S = {HHH , HHT , HTH , THH , HTT , THT , TTH , TTT}

∴ n (S) = 8

X = the number of heads.

∴ Range set of X = {0,1,2,3}

∴ P(X = 0) = P {TTT} = `1/8`

P (X = 1) = P {HTT , THT , TTH} = `3/8`

P (X = 2) = P {HHT , HTH , THH} = `3/8`

P (X = 3) = P {HHH} = `1/8`

Hence the probability distribution of X is as shown in the following table:

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