Paper 2, Section II, F

Probability | Part IA, 2015

Lionel and Cristiana have aa and bb million pounds, respectively, where a,bNa, b \in \mathbb{N}. They play a series of independent football games in each of which the winner receives one million pounds from the loser (a draw cannot occur). They stop when one player has lost his or her entire fortune. Lionel wins each game with probability 0<p<10<p<1 and Cristiana wins with probability q=1pq=1-p, where pqp \neq q. Find the expected number of games before they stop playing.

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