A game consist of a series of rounds In round 1 a random int

A game consist of a series of rounds. In round 1, a random integer is selected from the set {1, 2}, in round 2 a random integer is selected from the art {1, 2, 3}, and generally in round n, n greaterthanorequalto 3, a random integer is selected from the set {1, 2, ..., n+1}. You bet on number 2 in each of the rounds independently. What is the probability that you score no wins in the first n rounds? What is the probability that you play indefinitely and never win?

Solution

Here all the sets contain number 2 so therefore the probability to win the game is 1. And probability to loose the game is 0 if we bet a game on number 2.

No set contain number 0 and negative numbers. If we bet on these negative numbers od zero from the above sets then definitely the probability to loose the game is 1