Among employees at a retailer, there is a 15% chance that an employee will be ab

Question

Among employees at a retailer, there is a 15% chance that an employee will be absent from work for some reason. The floor manager has been talking with two randomly selected employees each day to get suggestions to improve sales. (a) What is the probability that the first employee he chooses to speak with is absent? (b) Describe the probability that the second employee he chooses to speak with is absent, assuming that the first employee is present, is it higher, lower, or the same as the probability in part (a)? (c) Should your answers to parts (a) and (b) match? Explain why or why not

Explanation / Answer

Let A and B denote the events of the two employees being absent.

P(A) = P(B) = 0.15

(a) Probability that the first employee he choses to speak with is absent P(A) = 15% = 0.15

(b) The probability that the second employee he choses to is absent given that the first is present = P(B|A')

Since the events are independent, P(B|A') = P(B).

Also P(B) = 0.15 = P(A)

Therefore, the probability that the second employee is absent given that the first is present is the same as the probability that the first one is absent.

(c) The answers in the two parts (a) and (b) must match as the outcome of the event of each employee being absent does not depend on the other or they are independent events..

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