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The probability that a person who undergoes kidney operation will recover is 0.5. Find the probability that of the six patients who undergo similar operations.a. None will recover. b. Half of them will recover. |
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Answer» Since, there are six patients n = 6 p = P(success) = 0.5 and q = 1 - p = 0.5 X ~ B(n = 6, p = 0.5) The p.m.f. of x is given as P(X = x) = nCx(p)x (q)n-x P(X = x) = P(x) = 6Cx (0.5)x (0.5)6-x, x = 0, 1, 2, 3, 4, 5, 6 a. P(none will recover) P(X = 0) = 6C0 (0.5)0 (0.5)6-0 = (1) (1) (0.5)6 = 0.015625 b. P(half of them will recover) P(X = 3) = 6C3 (0.5)3 (0.5)6-3 = \(\frac{6!}{3!.3!}\) (0.5)3 (0.5)3 = \(\frac{6\times5\times4\times3!}{3\times2\times1\times3!}\)(0.125) (0.125) = 20 x 0.015625 = 0.3125 |
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