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A game show offers contestants the following chance to win a car: There are three doors. A car is hidden behind one door, and goats are hidden behind each of the other doors. The contestant selects a door. The game show host then opens one of the doors not chosen to reveal a goat (there are two goats, so there is always such a door to open). At this point, the contestant is given the opportunity to stand pat (do nothing) or to choose the remaining door. Suppose you are the contestant, and suppose you prefer the expensive sports car over a not-so-expensive goat as your prize. What do you do?

(a) Suppose you decide to stand with your original choice. What are your chances of winning the car?

(b) Suppose you decide to switch to the remaining door. What are your chances of winning the car?

(c) Suppose you decide to flip a fair coin. If it comes up heads, you change your choice, otherwise, you stand pat. What are your chances of winning the car?

After I did the first part now I get a) 1/3, b) 2/3

So what about part.c? I just simply use 1/2(the chance to get head) multiply 1/3 and multiply 2/3?

Thom
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    This is the Monty Hall problem. – Zubin Mukerjee Nov 28 '13 at 23:29
  • I love this problem :-) Mind-puzzling the first time one encounters it, and so obvious after having worked it out. Also, there are some traps: for example, how does the host choose the opened door (when he can choose)? – Jean-Claude Arbaut Nov 28 '13 at 23:40
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    AFAIK, much of the confusion had to see with the way Marylin Idiot-Savant posed the problem. It was ill-posed as she explained it. – DBFdalwayse Nov 28 '13 at 23:50
  • If you KNOW BEFOREHAND that the game show host is going to offer you this choice, you should switch (answer to (a) and (b)): the odds of your first choice being the car is $1/3$. The host opened a second door with a goat behind it, so the odds of a car being behind that door is obviously $0$. That means the odds of the car being behind the third door is $2/3$. The answer to (c) is obviously $1/2$, unless the host is cheating. – Stefan Smith Nov 29 '13 at 00:59
  • I just simply use 1/2(the chance to get head) multiply 1/3 and multiply 2/3? – Thom Dec 01 '13 at 22:39

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