Question

A certain delivery service offers both express and standard delivery. 75% of parcels are sent by standard delivery, and 25% are sent by express. Of those sent standard, 80% arrive the next day, and of those sent express, 95% arrive the next day. A record of parcel delivery is chosen at random from the company's files.What is the probability that the parcel was shipped expressed and arrived the next day?

Answer 1

Answer:

The probability that the parcel was shipped expressed and arrived the next day = 0.2375 .

Step-by-step explanation:

We are given that a certain delivery service offers both express and standard delivery.

Let Proportion of parcels sent by standard delivery, P($A_1$) = 0.75

      Proportion of parcels sent by express delivery, P($A_2$) = 0.25

Let event B = Parcel arriving the next day

Also, Probability of parcel arriving the next day given it was sent through standard delivery, P(B/$A_1$) = 0.8

Probability of parcel arriving the next day given it was sent through express delivery, P(B/$A_2$) = 0.95

Now, Probability that the parcel was shipped expressed and arrived the next day = P($A_2$) * P(B/$A_2$) = 0.25 * 0.95 = 0.2375 .