Question 1201117: On a gameshow there are n ∈ N doors. Behind one of them is a prize and behind the others there is nothing. The gameshow host knows which door the prize is behind, but the contestant doesn’t. The rules of the game are as follows:
The contestant chooses k < n doors. The host then opens l < k of the doors that the contestant chose and m < n − k of the doors that the contestant did not choose, to reveal that the prize is not behind them. The contestant then gets to open any one of the remaining doors and claim whatever is behind that door.
Suppose that you are a contestant on this gameshow, and you wish to choose between two strategies:
• Strategy 1: Choose k distinct doors uniformly at random in the first step, and then in the second round, select (independently, and uniformly) one of the doors chosen in the first step that the host didn’t open.
• Strategy 2: Choose k distinct doors uniformly at random in the first step, and then in the second round, select (independently, and uniformly) one of the doors not chosen in the first step that the host didn’t open.
Which of the two strategies is better? (Your answer may depend on n, k, l, m).
Answer by ikleyn(52781)   (Show Source):
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