Suppose that a friend is helping put on a fundraiser for the local animal shelte

Question

Suppose that a friend is helping put on a fundraiser for the local animal shelter. One activity is a game using a bowl that contains six green marbles and eight blue marbles. To play the game, each person draws two marbles without replacement (and without looking). If both marbles are green, the player wins $25. If not, the player must donate $10 to the animal shelter. The marbles are then replaced for the next player.

a. Calculate the expected value of the game for the player.

b. Suppose that the marble game is played 350 times. How much money would you expect to be donated to the animal shelter?

Explanation / Answer

a. There are four cases

The probability that the first marble is green = 6/14.

Probability that the second marble is also green = 5/13.

=> Probability that both marbles are green = 6/14 * 5/13 = 0.1648.

Expected value = 0.1648 * $25 - (1 - 0.1648) * $10 = -4.2320$.

b. Expected donation to the animal shelter after 350 games

= 350 * 4.2320$ = 1481.2$.

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