Difference between revisions of "2023 AMC 12A Problems/Problem 7"
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There are <math>4</math> cases where her running total can equal <math>3</math>: | There are <math>4</math> cases where her running total can equal <math>3</math>: | ||
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1. She rolled <math>1</math> for three times consecutively from the beginning. Probability: <math>\frac{1}{6^3} = \frac{1}{216}</math> | 1. She rolled <math>1</math> for three times consecutively from the beginning. Probability: <math>\frac{1}{6^3} = \frac{1}{216}</math> | ||
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2. She rolled a <math>1</math>, then <math>2</math>. Probability: <math>\frac{1}{6^2} = \frac{1}{36}</math> | 2. She rolled a <math>1</math>, then <math>2</math>. Probability: <math>\frac{1}{6^2} = \frac{1}{36}</math> | ||
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3. She rolled a <math>2</math>, then <math>1</math>. Probability: <math>\frac{1}{6^2} = \frac{1}{36}</math> | 3. She rolled a <math>2</math>, then <math>1</math>. Probability: <math>\frac{1}{6^2} = \frac{1}{36}</math> | ||
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4. She rolled a <math>3</math> at the beginning. Probability: <math>\frac{1}{6}</math> | 4. She rolled a <math>3</math> at the beginning. Probability: <math>\frac{1}{6}</math> | ||
Revision as of 19:58, 9 November 2023
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 
?
Solution 1
There are cases where her running total can equal :
1. She rolled 
for three times consecutively from the beginning. Probability: 
2. She rolled a , then 
. Probability: 
3. She rolled a , then . Probability:
4. She rolled a at the beginning. Probability: 
Add them together to get 
~d_code
