Problem:
Janet rolls a standard -sided die times and keeps a running total of the numbers she rolls. What is the probability that at some point, her running total will equal ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
We divide this problem into cases, depending on how Janet gets to the :
Janet rolls a total of 3 if she starts by rolling 111, 12, 21, or 3. These initial sequences of rolls occur with probability , and , respectively. Adding these probabilities gives
The problems on this page are the property of the MAA's American Mathematics Competitions