Question

Morgan is playing a board game that requires three standard dice to be thrown at one time. Each die has six sides, with one of the numbers 1 through 6 on each side. She has one throw of the dice left, and she needs a 17 to win the game. What is the probability that Morgan wins the game (order matters)?
A.) 1/108
B.) 1/216
C.)1/64
D.) 1/72

Answer 1

the sums, 3 through 18, are possible but with different probabilities.
all you need to do is count the number of ways to get a 17 and then divide by 216 (\(=6^2\), the total number of possible outcomes).
as it turns out, there are only 3 ways to get a 17:
5, 6, 6
6, 5, 6
6, 6, 5

where the numbers are the numbers shown on the 1st, 2nd and 3rd die, resp.

so the probability you seek is...?