# Solved: (Three-Door Game) Behind one of the 3 doors (A, B and C) is a prize of \$3M. Follow the

(Three-Door Game) Behind one of the 3 doors (A, B and C) is a prize of \$3M. Follow the three steps below to play. 1. You choose a door. 2. The host opens another door with no prize, but cannot open the door you chose. 3. You can either stick to the door you chose first or switch to the other unopened door. Suppose you choose door A and then the host opens door B (another door with no prize). Would you stick to door A (you chose first) or the other unopened door (C)? Set up original and flipped probability trees with all probabilities attached. (Hint: Define the events: AP = A with prize, BP = B with prize, CP = C with prize, bo = B opened and co = C opened.) 1 (Three-Door Game) Find the prior probabilities below. (a) Probability that door A is with the prize [Answer format: three decimal places] (b) Probability that door B is with the prize [Answer format: three decimal places] (c) Probability that door C is with the prize [Answer format: three decimal places] Write your answer(s) as 0.123, 0.456, 0.789