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?

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() = 0.75

      Proportion of parcels sent by express delivery, P() = 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/) = 0.8

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

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

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