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
