# Math Help - Probability question

1. ## Probability question

The following was confusing me so any help would be greatly appreciated!

A box contains 8 white, 4 black, and 2 red balls. We win 2 coins for each black ball drawn and lose 1 coin for each white ball drawn. We choose 3 balls from the box. X denotes our winnings. Find the mass probability function of X.

2. ## Hope this helps

This is one of those situations were it really doesn't hurt to write out all of the possibile permutations ...

I assume you are drawing the balls without replacement the problem changes a bit if you replace the balls (it allows for one more permutation)

Once you find all 26 permutations the resulting pmf can be found by tabulation. (There are other ways to do this but I like this way when it works) The following table has the X values or payout across the top and the value of the pmf across the bottom. Each of the numerators is simply the frequency with which each payout appeared among the permutations that were possible.

-3

-2

-1

0

1

2

3

4

6

1/26

3/26

3/26

3/26

6/26

3/26

4/26

2/26

1/26