# Probability and the Gamblers Net Gain

A box has three red ball and five green balls. A gambler bets 1.00 on red. A ball is randomly chosen. The gambler wins 1.00 if the ball is red, otherwise he loses 1.00. He will play this game 100 times.

I need to know what the value for the gamblers net gain is. I also need to find the SE for the gamblers net gain. Also what is the chance/percent the gambler will win between $0 and $5?

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#### Solution Preview

This is a question of Binomial Distribution, the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p.

In this case p = prob(red) = number of red balls/ total balls = 3/(3+5) = 3/8 = 0.375

N = 100

The expected number of wins of the 100 times is the mean of the distribution.

M = N*p = 100 * 0.375 = 37.5

That is, he will gain $37.5, ...

#### Solution Summary

In this solution the author provides a thorough calculation breakdown to arrive at the desired answer.