A game show has n doors, behind one of which is a prize. A contestant selects k doors, and the host opens l of the chosen doors and m unchosen doors, revealing no prize. The contestant can then open one remaining door. Strategy 1 has the contestant select another of their original k doors, while Strategy 2 has them select an unchosen door. The best strategy depends on the values of n, k, l, and m.

1. 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 doesnt.
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 didnt 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 didnt
open. Which of the two strategies is better? (Your answer may depend on n, k, l, m).