At a certain company, 60% of the employees are certified to operate machine A, 3

Question

At a certain company, 60% of the employees are certified to operate machine A, 30% are certified to operate machine B, and 10% are certified to operate both machine A and machine B. Let A denote the event that a randomly chosen employee is certified to operate machine A, and let B denote the event that a randomly chosen employee is certified to operate machine B.

(a) Find the probability that a randomly chosen employee is certified to operate at least one of machines A and B.

(b) Find the probability that a randomly chosen employee is certified to operate one of machines A and B but not both.

(c) Find the probability that a randomly chosen employee is certified to operate machine A but not machines B.

(d) Find the probability that a randomly chosen employee is certified to operate at least one of machines A and B.

Explanation / Answer

a) P(least one of machines A and B) = 0.60+0.30-0.10 = 0.80

b) P(one of machines A and B but not both.) = (0.60-0.10)+(0.30-0.10) = 0.70

c) P(A but not machines B.) = 0.60-0.10 = 0.50

d) P(least one of machines A and B) = 0.60+0.30-0.10 = 0.80

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