Maharashtra State BoardHSC Arts 12th Board Exam
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A Fair Coin is Tossed 9 Times. Find the Probability that It Shows Head Exactly 5 Times. - Mathematics and Statistics

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Sum

A fair coin is tossed 9 times. Find the probability that it shows head exactly 5 times.

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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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