A local delivery service offers both express and standard delivery. Seventy-two

Question

A local delivery service offers both express and standard delivery. Seventy-two percent of parcels are sent by standard delivery and the remainder are sent by express. Of those set standard, 83% arrive the next day and of those sent express 97% arrive the next day. The tracking information of a parcel delivery is chosen at random from the company's files. a. What is the probability that the parcel was shipped express and arrived the next day? b. What is the probability that the parcel arrived the next day? c. Given that the package arrived the next day, what is the probability that it was sent express?

Explanation / Answer

A) P(parcel was shipped by express and arrived the next day) = 0.28x0.97 = 0.2716

B) P(parcel arrived the next day) = 0.28x0.97 + 0.72x0.83 = 0.8692

C) P(sent by express | arrived the next day) = P(sent by express and arrived the next day) / P(arrived the next day)

M= 0.2716/0.8692 = 0.3125

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