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?

The probability that she wins exactly once before she loses her initial capital is 0.243.

Step-by-step explanation:

The gambler commences with $30, i.e. she played 3 games.

Let X = number of games won by the gambler.

The probability of winning a game is, p = 0.10.

The random variable X follows a Binomial distribution, with probability mass function:

Compute the probability of exactly one winning as follows:

Thus, the probability that she wins exactly once before she loses her initial capital is 0.243.

lockers 1, 4, 9, 16, 25, 40, and 49 are open

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