# Question: A gambler plays a game of chance where he wins

A gambler plays a game of chance where he wins $ 1 with probability ρ and loses $ 1 with probability 1–p each time he plays. The number of games he plays in an hour, N, is a random variable with a geometric PMF, PN( n) = ( 1 – q) qn – 1 n = 1,2, 3, …,.

(a) What is the PGF of the gambler’s total winnings after playing for an hour?

(b) What is the probability that the gambler has not lost any money after an hour if p = 0.48 and q = 7/ 8?

(a) What is the PGF of the gambler’s total winnings after playing for an hour?

(b) What is the probability that the gambler has not lost any money after an hour if p = 0.48 and q = 7/ 8?

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