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Question
A fair coin is tossed 9 times. Find the probability that it shows head exactly 5 times.
Solution
Let X = no. of heads shows
n = 9 p = `1/2` q = `1/2`
P(X = x) = `""^nC_x p^n.(q)^(n-x)` X = 0,1.....n
P(X = 5) = `""^9C_5 (1/2)^5(1/2)^4`
`= (9xx8xx7xx6)/(4xx3xx2xx1) xx 1/2^9`
`= 3024/24 xx 1/2^9`
`= 126/2^9`
`= 126/512`
= 0.2460
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