There are 101 rooms, starting at room 1. The probability of finding $3 in a room is 50%, given that the room (x-1) did not have money in it, and that rooms (x-3) and (x-2) did. Rooms 1-3 have 50% probability. The room you are in is room x. Also, there is a +1% chance that every tenth room will have $3. What is the probability that 26 rooms will have $3? Also, if you pay $20 to play, is it worth it to play the game?

Question

There are 101 rooms, starting at room 1. The probability of finding $3 in a room is 50%, given that the room (x-1) did not have money in it, and that rooms (x-3) and (x-2) did.  Rooms 1-3 have 50% probability. The room you are in is room x.  Also, there is a +1% chance that every tenth room will have $3.  What is the probability that 26 rooms will have $3?  Also, if you pay $20 to play, is it worth it to play the game?

dan815 · Answer

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