Question

A game involves rolling two dice, one after the other. jenny wins the game if both dice are even. Henry wins the game if either die is a 4.

-How may different outcomes are there ?
-list the outcomes for Jenny
-list the outcomes for Henry
-What is the probability that Jenny wins?
-What is probability that Henry wins?
-Is the game fair? why
-Are there any outcomes where the game will result in a tie ?

Answer 1

A. The total outcomes would simply be the product of the number of sides of the two dice, that is:

Total different outcomes = 6 * 6

Total different outcomes = 36

B. The combinations that both dice are even are:

2 – 2, 4 – 4, 6 – 6, 2 – 4, 2 – 6, 4 – 2, 4 – 6, 6 – 2, 6 – 4

So 9 combinations for Jenny

C. The combinations that at least one die is a 4 are:

4 – 4, 4 – 1, 4 – 2, 4 – 3, 4 – 5, 4 – 6, 1 – 4, 2 – 4, 3 – 4, 5 – 4, 6 - 4

So 11 combinations for Henry

D. The probability that jenny wins would simply be the ratio of the number of combinations for Jenny over the total number of combinations, that is:

P (Jenny) = 9 / 36 = 0.25 = 25%

So there is a 25% chance that Jenny will win.

E. The probability that Henry wins would simply be the ratio of the number of combinations for Henry over the total number of combinations, that is:

P (Henry) = 11 / 36 = 0.3056 = 30.56%

So there is a 30.56% chance that Jenny will win.

F. No the game is not fair because Henry has a higher chance of winning than Jenny. For it to be fair, they should have the same probability of winning.

G. We can see that there are actually combinations in which both Jenny and Henry would win. These are:

4 – 4, 4 – 2, 4 – 6, 2 – 4, 6 – 4

So there are 5 combinations in which both of them would win.

So the chance of being tie is:

P(tie) = 5 / 36 = 0.1389 = 13.89%

Hence a 13.89% chance of getting a tie