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Calculating probabilities of a dice game

Suppose someone gives you 9 to 2 odds that you cannot roll two even numbers with the roll of two fair dice. This means you win $9.00 if you succeed and you lose $2.00 if you fail. What is the expected value of this game to you? Should you expect to win or loose the expected value in the first game? What can you expect if you play 100 times? Explain (a table will be helpful in finding the required probabilities).

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+7=11
6 6+1=7 6+2=8 6+3=9 6+4=10 6+5=11 6+6=12
A- What is the expected value of this game to you? $___
Should you expect to win (or lose) the expected value in the first game? Yes or No
B- What can you expect if you play 100 times ? $____
C- Explain this result- averaged over 100 games, you should expect to (win or lose) $___.

Solution Preview

Of the above 36 possible outcomes, 9 involve two even numbers. Thus the probability of rolling two ...

Solution Summary

The solution computes the odds of winning a game involving dice as well as our expected winnings per play.

$2.19