One concern of a gambler is that she will go broke before

Chapter 3, Problem 194SE

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QUESTION:

Problem 194SE

One concern of a gambler is that she will go broke before achieving her first win. Suppose that she plays a game in which the probability of winning is .1 (and is unknown to her). It costs her $10 to play and she receives $80 for a win. If she commences with $30, what is the probability that she wins exactly once before she loses her initial capital?

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QUESTION:

Problem 194SE

One concern of a gambler is that she will go broke before achieving her first win. Suppose that she plays a game in which the probability of winning is .1 (and is unknown to her). It costs her $10 to play and she receives $80 for a win. If she commences with $30, what is the probability that she wins exactly once before she loses her initial capital?

ANSWER:

Solution:

Step 1 of 2:

One concern of a gambler is that she will go broke before achieving her first win.

If she plays a game in which the probability of winning is 0.1, it costs her $10 to play and $80 for a win.

We have to find the probability that she wins once before she loses her final capital.


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