Theory question 113
ProbabilityThe probabilities that Kofi, Kwasi and Ama will pass a certain examination are 9/10, 4/5 and x respectively. If the probability that only one of them will pass examination is 9/50, find the: (a) value of x; (b) probability that at least one of them will pass examination.
Show the model answer
Model answer
(a) Only one passes: (9/10)(1/5)(1 − x) + (1/10)(4/5)(1 − x) + (1/10)(1/5)x = 9/50.
9(1 − x) + 4(1 − x) + x = 9, so 13 − 12x = 9 and x = 1/3.
(b) P(all fail) = (1/10)(1/5)(2/3) = 1/75; P(at least one) = 74/75 ≈ 0.987.
Explanation
List the three 'only one passes' cases and add them.