申論題

Let P(Ai) be the probability that the car is behind door no, i. Thus, the probability that the car is behind door no. I is P(A₁). Let P(B) be the probability that the contestant picks door no. j, and let P(C_k) be the probability that the host picks door no. k. Note that P(C3lA2, B1) is the probability that the host opens door no. 3 after the contestant picked door no. 1, and the car is behind door no. 2.

(x) Express the probability that the ca ar is behind door no. 2 given that the contestant picked door no. I and the host opened door no. 3 using the form P(X|Y,Z), but replacing with A_i, B_j, and C_k, accordingly. (3 pt)

 Note that