Question

A gambler enters a casino with an initial fortune of HK$100. Then, on each successive gamble, he will pay $1 to play and either wins $1 or loses $1 with the probabilities 49% and 51%, respectively. 2 The probability of winning or losing a gamble is independent of the past gambles. What is the probability that he has not run out of money in 100 gambles?

Note: I have something in mind but I want to be sure that it is correct. We take out the chances that he runs out of all the money in the 100th gambles (binomial distribution) and then subtract it by 1. Is this okay?

Answer 1