Two dice are rolled. If the total is 2, then player A receives 4 points. If the total is 8, then player B receives 3 points. Find the expected value for each player.

Question

zarkon · Answer

what are you stuck on?

anonymous · Answer

i don't know how to set up the problem.

anonymous · Answer

If the total of the dice is 2, that means that one die is a 1 and the other die is also a 1.  The probability of that happening is 1/36 (from 1/6 x 1/6).  The expected value is the sum of the probabilities of each occurence times its value.

So, for player A, you have (1/36)(4) + (35/36)(0) = 1/9

This is assuming that player A gets no points for any other rolls.

Are you with me so far?

anonymous · Answer

yes! loud and clear :)

anonymous · Answer

For player B, you have to start by seeing what the probability of rolling an 8 is.  You will have the following combinations on the dice: 

2,6     3,5     4,4    5,3    6,2

which is 5 rolls out of 36 so the P(8) = 5/36

And player B's expected value is :

(5/36)(3) + (31/36)(0) = 5/12

Again, assuming that player B gets no points for any other rolls, similar to the assumption for player A.

Is this making sense to you?

anonymous · Answer

Notice that for player A that    1/36 + 35/36 = 1   and that exhausts all possibilities.

Similarly for player B,      5/36 + 31/36 = 1

anonymous · Answer

thank you so much tcarroll010!!!! i understood everything!!!

anonymous · Answer

So, the learning points aer that the expected value is the sum of the individual probabilites (times their values) for all possible outcomes.

anonymous · Answer

And you're quite welcome!  Nice working with you!