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

When three coins is tossed, possible outcomes to get Heads are,

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

Here,

T→Tail H→Head

Consider X be the difference between the number of heads and the number of tails

Draw a table for the different sample space:

X	Outcomes	Number of Outcomes	P( X )
0	{ TTT }	1	1 8
1	{ THT,TTH,HTT }	3	3 8
2	{ HHT,HTH,THH }	3	3 8
3	{ HHH }	1	1 8

So the probability distribution:

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

Therefore, the mean number is given by,

μ= ∑ i=1 n X i P i =( 0× 1 8 )+( 1× 3 8 )+( 2× 3 8 )+( 3× 1 8 ) = 12 8 = 3 2

Thus, the mean number of heads in three tosses of a fair coin is 3 2 .