6. Suppose you are a contestant on a TV game show where a new car is hidden behind exactly one of N doors, with probability Pn that the car is behind door n = 1,..., N. You select door number 1. If the car is behind door number 1, you then win the car with probability Q. Obviously, if the car is behind any other door, you cannot win. (a) Find the conditional probability that the car was in fact behind door number 1 given that you did not win. Hint: begin by defining events En = "the car is behind door n" and W = "you win". What are Pn and Q in terms of these events? (b) Given that you did not win, find the probability that the car was behind door number n, n = 2, . .., N