Question

You are a contestant on the all new "Let’s Make A Deal" with Montana Hill. Montana brings you up to play the 6 doors game. Behind one door is $1200. Behind another door is $120. Behind the other 4 doors is $0. The game works just like Monty’s version in that the prizes are randomly distributed and, after you choose a door, Montana will open a door (which will always hide $0) and give you the opportunity to switch your choice.(A) What is your probability of getting a prize (of either $1200 or $120) if you switch your guess after Montana opens one door?(B) After playing the game, Montana gives you the opportunity to buy a chance to play again. What is the fair price you should be willing to pay to play this game?

Answer 1

A. The probability of getting a prize (of either $1200 or $120) if you switch your guess after Montana opens one door is 0.6

B. The fair price you should be willing to pay to play this game is $264

Explanation:

A. According ot the given data Let A be the event of wining a prize

Let B the event of losing a prize

P(A)=2/6C1=2/6=1/3

P(B)=1-P(A)=2/3

Hence, after opening the door:

P(A I B)=P(A∩B)/P(A)

P(A∩B)=2/5

P(A I B)=2/5/2/3

P(A I B)=0.6

The probability of getting a prize (of either $1200 or $120) if you switch your guess after Montana opens one door is 0.6

B. The fair price you should be willing to pay to play this game=∑(expected prize) probability

The fair price you should be willing to pay to play this game=1200*1/5 + 120*1/5 + 0*3/5

The fair price you should be willing to pay to play this game=$264

The fair price you should be willing to pay to play this game is $264