Respuesta :
Answer:
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 [tex]D_{A}[/tex] = destination is in Zone A and [tex]D_{B}[/tex] = destination is in Zone B.
Given:
The probabilities are:
[tex]P(D_{A}|A)=0.65\\P(D_{B}|A)=0.35\\P(D_{A}|B)=0.45\\P(D_{B}|B)=0.55[/tex]
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:
[tex]E(Profit\ in\ A)=E(A-A)\times P(D_{A}|A)+E(A-B)\times P(D_{A}|B)\\=(7\times 0.65)+(12\times0.35)\\=8.75[/tex]
Determine the expected profit earned in Zone B as follows:
[tex]E(Profit\ in\ B)=E(B-B)\times P(D_{B}|B)+E(B-A)\times P(D_{B}|A)\\=(8\times 0.45)+(12\times0.55)\\=10.20[/tex]
The total expected profit is:
[tex]E (Profit)=E(Profit\ in\ A)\times P(Zone A) + E(Profit\ in\ B)\times P(Zone B)\\=(8.75\times0.50)+(10.20\times 0.50)\\=9.475\\\approx9.50[/tex]
Thus, the taxi drivers average profit per trip is $9.50.
