Objective: Construct a probability distribution and use it to find the expected value of the game.

Introduction: Here's the game: there are two boxes with four balls each. To play, you put on a blindfold and then pick one ball at random from each box.

There are two red, one blue and one green ball in the box on the left. There are two blue, one red and one green ball in the box on the right.

Payouts:

$0 if the balls are different colors,

$0.50 if they are both red,

$1 if they are both blue, and

$16 if they are both green.

Question:

If the game costs $1 to play, would you expect to gain or lose money on average? And how much?

In your solution, you must show:

How you compute the probability that payout is $0.

How you compute the probability that payout is $0.50.

How you compute the probability that payout is $1.

How you compute the probability that payout is $16.

Summarize the data into a probability table.

Compute the expected value.

Remember to account for the $1 you pay to play the game.

Your conclusion.