Question

A certain delivery service offers both express and standard delivery. Seventy-five percent 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 a parcel delivery is chosen at random from the company's files.

Answer 1

Probability, P(n) = 3/8

Explanation: Let standard delivery be S and express delivery be E.

I) When the parcels were sent:

S(n) = 75/100 and E(n) = 25/100

II) When the parcels arrived:

S(n)← = 80/100 and E(n)← = 95/100

The probability a record of a parcel delivery is chosen, P(n) = S(n)*E(n) + E(n)*S(n) = 75/100*25/100 + 25/100*75/100

P(n) = 3/16 + 3/16 = 6/16

∴ P(n) = 3/8