A bank that had a coffee machine and a plate of cookies for waiting customers, i

Question

A bank that had a coffee machine and a plate of cookies for waiting customers, it was determine that the probability that a customer's drank coffee was 0.72, the probability that a customer had a cookie was 0.58, and the probability that a customer had both coffee and a cookie was 0.37. a. What is the probability that a randomly selected customer did not have a cookie? b. What is the probability that a randomly selected customer drank coffee or had a cookie? c. What is the probability that a randomly selected customer did not have coffee and did not have a cookie (they had neither)? d. What is the probability that a randomly selected customer had coffee and did not have a cookie? Would this be considered unusual? e. What is the probability that a randomly selected customer did not have coffee or did not have a cookie?

Explanation / Answer

(a) Probability = 1 - 0.37 = 0.63

(b) Probability = 0.72 + 0.58 - 0.37 = 0.93

(c) P(Neither coffee nor cookie) = 1 - P(Either coffee or cookie) = 1 - 0.93 = 0.07

(d) P(Only coffee) = P(Coffee) - P(Both coffee and cookie) = 0.72 - 0.37 = 0.35

This is not unusual since the probability > 0.05

(e) P(Not coffee) = 0.38, P(Not cookie) = 0.42, P(neither coffee nor cookie) = 0.07

P(Not coffee or not cookie) = 0.38 + 0.42 - 0.07 = 0.73

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