Question

In a game you roll two fair dice. If the sum of the two numbers obtained is 3,4,9,10 or 11 you win $20. If the sum is 5,6,7 or 8 you pay $20. However if the scores on the dice are the same no one is required to pay.

(a) Construct a probability distribution table for the event

(b) Determine the expected outcome of this game. Is it fair?

(c) What should your winnings be for the game to be fair?

Answer 1

I will start it for you. Most numbers can be obtained in more than one way. 2 and 12, the only no pay numbers, can only be obtained one way.

3 = 2,1 or 1,2 = 2 ways
4 = 2,2 or 3,1 or 1,3 = 3 ways
5 = 3,2 or 2,3 or 1,4 or 4,1 = 4 ways
etc.