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.

Answer 1

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) = ⁶C_x (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`