A sports bar hosts a gaming night where students play casino games using play mo

Question

A sports bar hosts a gaming night where students play casino games using play money. A business major has $1500 in play money and decides to test a strategy on the roulette wheel. The minimum bet is $100 with no maximum. He decides to bet that the ball will land on red each time the wheel is spun. On the first bet, he bets the minimum. For each consecutive spin of the wheel, he doubles his previous bet. He decides beforehand that he will play roulette the exact number of times that his cash stock would allow if he lost each time consecutively. What is the probability that he will run out of money before leaving the table?

Explanation / Answer

Let the probability of ball landing on red be p and the probability of ball not landing on red be q.

And let pn denote the probabiltity of winning on the nth spin.

So qn denotes the probabiltity of not winning on the nth spin.

So P=P[Business major will run out of money]

= (p1 x q2) + (p1 x p2 x q3) + (p1 x p2 x p3 x q4)

And then he will reach his limit of $1500.

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