2023 AMC 12A Problems/Problem 7

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

2023 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 4
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All AMC 12 Problems and Solutions

2023 AMC 10A (Problems • Answer Key • Resources)
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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2023 AMC 12A Problems/Problem 7

Problem

Solution 1

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