Question

Suppose someone gives you 8 to 2 odds that you cannot roll two even numbers with the roll of two fair dice. This means you win ​$8 if you succeed and you lose ​$2 if you fail. What is the expected value of this game to​ you? Should you expect to win or lose the expected value in the first​ game? What can you expect if you play​​​​​​​ 200 ​times? Explain.​(The table will be helpful in finding the required​ probabilities.)

Table of outcomes and sums for the roll of two dice

	1	2	3	4	5	6
1	1+1=2	1+2=3	1+3=4	1+4=5	1+5=6	1+6=7
2	2+1=3	2+2=4	2+3=5	2+4=6	2+5=7	2+6=8
3	3+1=4	3+2=5	3+3=6	3+4=7	3+5=8	3+6=9
4	4+1=5	4+2=6	4+3=7	4+4=8	4+5=9	4+6=10
5	5+1=6	5+2=7	5+3=8	5+4=9	5+5=10	5+6=11
6	6+=7	6+2=8	6+3=9	6+4=10	6+5=11	6+6=12

What is the expected value of this game to​ you?

​$__?

Should you expect to win​ (or lose) an amount equal to the expected value in the first​ game?

Yes, you can expect to win​ (or lose) the expected value in the first game.

No, the outcome of one game cannot be predicted.

What can you expect if you play​​​​​​​ 200​​​​​​​ times? $___

Explain this result.

Averaged over 200 ​games, you should expect to __ ​$__.

Answer 1