Behind one of the 3 doors (A, B and C) is a prize of $3M. Follow the three steps

Question

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. (Three-Door Game) Find the posterior probabilities below. (a) Probability that door A is with the prize given door B is opened [Answer format: two decimal places] (b) Probability that door C is with the prize given door B is opened [Answer format: two decimal places] (c) Probability that door A is with the prize given door C is opened [Answer format: two decimal places] (d) Probability that door B is with the prize given door C is opened [Answer format: two decimal places] Write your answer(s) as 0.12, 0.34, 0.56, 0.78 ________

Explanation / Answer

as door A ,B,C all three has probability to contrain prize =1/3.

Once any of door from B and C openned the probabilty behind left door to contain prize remains 1/3 while probabilty with door A to have prize becomes 2/3 due to posterior information available.

a)

probability =2/3 =0.66

b) probability =1/3 =0.33

c) probability =2/3=0.66

d) probability =1/3 =0.33

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