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Question
The probability that a person who undergoes a kidney operation will be recovered is 0.5. Find the probability that out of 6 patients who undergo similar operation half of them recover.
Solution
Let X denote the number of patients recovered.
P(patient recovers) = p = 0.5
∴ q = 1 – p = 1 – 0.5 = 0.5
Given, n = 6
∴ X ~ B(6, 0.5)
The p.m.f. of X is given by
P(X = x) = 6Cx (0.5)x (0.5)6–x, x = 0, 1, …, 6
P(half of them recover) = P(X = 3)
= 6C3 (0.5)3 (0.5)3
= `(6!)/(3! xx 3!) xx 1/2^6`
= `(6 xx 5 xx 4)/(3 xx 2) xx 1/64`
= `20/64`
= `5/16`
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