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jmc

counting and probability senior

Problem

A fair, twenty-faced die has of its faces numbered from through and has one blank face. Another fair, twenty-faced die has of its faces numbered from through and through and has one blank face. When the two dice are rolled, what is the probability that the sum of the two numbers facing up will be Express your answer as a common fraction.
Solution
If both dice were numbered through we could get a sum of in the following ways: This is a total of ways. However, the first die does not have a face with so we must remove the possibility of rolling Also, the second die does not have a face with so we must remove the possibility of rolling This leaves possible ways to roll There are a total of possible rolls, so the final probability is:
Final answer
\frac{3}{80}