A taxi driver provides service in two zones of a city. Fares picked up in zone A will have destination in zone A with probability 0.65 or in zone B with probability 0.35. Fares picked up in zone B will have destinations in zone A with probability 0.45 or in zone B with probability 0.55. The driver's expected profit for a trip entirely in zone A is $7; for a trip entirely in zone B is $8; and for a trip that involves both zones is $12. Find the taxi drivers average profit per trip.

The taxi drivers average profit per trip is $9.50.

Step-by-step explanation:

The taxi driver provides services in Zone A and Zone B.

Let = destination is in Zone A and = destination is in Zone B.

Given:

The probabilities are:

The Expected profit are:

If the trip is entirely in Zone A the expected profit is, E (A - A) = $7.

If the trip is entirely in Zone B the expected profit is, E (B - B) = $8.

If the trip involves both the zones the expected profit is,

E (A - B) = E (B - A) = $12.

Determine the expected profit earned in Zone A as follows:

Determine the expected profit earned in Zone B as follows:

The total expected profit is:

Thus, the taxi drivers average profit per trip is $9.50.

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.