# A Fair Coin is Tossed 9 Times. Find the Probability that It Shows Head Exactly 5 Times. - Mathematics and Statistics

Sum

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

Concept: Bernoulli Trials and Binomial Distribution
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