2023 AMC 12A Problems/Problem 7

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Problem

Janet rolls a standard $6$-sided die $4$ times and keeps a running total of the numbers she rolls. What is the probability that at some point, her running total will equal $3$?

Solution 1

There are $4$ cases where her running total can equal $3$:

1. She rolled $1$ for three times consecutively from the beginning. Probability: $\frac{1}{6^3} = \frac{1}{216}$

2. She rolled a $1$, then $2$. Probability: $\frac{1}{6^2} = \frac{1}{36}$

3. She rolled a $2$, then $1$. Probability: $\frac{1}{6^2} = \frac{1}{36}$

4. She rolled a $3$ at the beginning. Probability: $\frac{1}{6}$

Add them together to get $\boxed{\textbf{(B)} \frac{49}{216}}.$

~d_code

See Also

2023 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions
2023 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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