Question

A taxi driver provides service in two zones of a city. Fares picked up in zone A will have destinations in zone A with a probability of 0.6 or in zone B with a probability of 0.4. Fares picked up in zone B will have destinations in zone A with a probability of 0.3 or in zone B with a probability of 0.7. The driver's expected profit for a trip entirely in zone A is 6; for a trip entirely in zone B is 8, and for a trip that involves both zones is 12. Find the taxi driver's average profit per trip.

Answer 1

The taxi driver's average profit per trip is 4.4.

Explanation:

Probability of fares picked up in zone A with destinations in zone A = 0.6

Probability of fares picked up in zone A with destinations in zone B = 0.4

Probability of fares picked up in zone B with destinations in zone A = 0.3

Probability of fares picked up in zone B with destinations in zone B = 0.7

The driver's expected profit for a trip entirely in zone A = 6

The driver's expected profit for a trip entirely in zone B = 8

The driver's expected profit for a trip involving both zones is 12

The taxi driver's average profit per trip:

zone A with destinations in zone A = 0.6 * 6 = 3.6

zone A with destinations in zone B = 0.4 * 12 = 4.8

zone B with destinations in zone A = 0.3 * 12 = 3.6

zone B with destinations in zone B = 0.7 * 8 = 5.6

Total profit expected for 4 trips = 17.6

Average profit per trip = 4.4 (17.6/4)