Question

Find the mean number of heads in three tosses of a fair coin.

Answer 1

The sample space of given experiment is 

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

Let X denotes the no. of heads in three tosses of a fair coin 

Here, X is random which may have values 0, 1, 2, 3.

Now, P(X = 0) = 1/8,P(X = 1) = 3/8

P(X = 2) = 3/8, P(X = 3) = 1/8

Therefore, Probability distribution is

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

∴ Mean number (E(x)) = ∑p_ix_i = 0 x 1/8 + 1 x 3/8 + 2 x 3/8 + 3 x 1/8

= (3 + 6 + 3)/8 = 12/8 = 3/2 = 1.5