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Question

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

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Solution

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

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

Here,

TTail HHead

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

Draw a table for the different sample space:

XOutcomesNumber 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 .


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