Question

1. Airlines often charge a fee for passengers to select their own seat. To avoid the fee, a prospective passenger allows his seat to be selected randomly. Let A denote the event that the selected seat is an aisle seat, let B denote the event that it is a middle seat, let C denote the event that it is a window seat and let D denote the event that the selected seat is in the back half of the plane. Suppose P(A) = 0.31, P(B)=0.52, P(C)= 0.17. P(D|B) = 0.35, P(D|C) = 0.63, P(D|A) = 0.54.
   1. P(D|B) indicates (choose one)
      1. The probability that the seat is in the back half of the plane and is a middle seat.
      2. The probability that the seat is in the back half of the plane given that it is a middle seat.
      3. The probability that the seat is a middle seat given that it is in the back half of the plane.
      4. The probability that the seat is in the back half of the plane and is not a middle seat.

B.Find the probability that the seat selected is a middle seat and in the back half of the plane

C. Find the probability that the seat is in the back half of the plane.

D.Find the probability that the seat is a window seat given that it is in the back half of the plane.

E.Find the probability that the seat is in the front half of the plane given that it is a window seat.

F. Let E denote the event that the selected seat is on the right side of the plane. If P(E)= 0.45 and event E is independent of whether the seat is an aisle, middle, or window seat, find the probability that the selected seat is a window seat and on the right side of the plane.

Answer 1