Difference between revisions of "2023 AMC 12A Problems/Problem 7"
(Created page with "Hey the solutions will be posted after the contest, most likely around a couple weeks afterwords. We are not going to leak the questions to you, best of luck and I hope you ge...") |
|||
| Line 1: | Line 1: | ||
| − | + | ==Problem== | |
| − | - | + | Janet rolls a standard <math>6</math>-sided die <math>4</math> times and keeps a running total of the numbers |
| + | she rolls. What is the probability that at some point, her running total will equal <math>3</math>? | ||
| + | |||
| + | ==Solution 1== | ||
| + | |||
| + | There are <math>4</math> cases where her running total can equal <math>3</math>: | ||
| + | 1. She rolled <math>1</math> for three times consecutively from the beginning. Probability: <math>frac{1}{6^3} = frac{1}{216} | ||
| + | 2. She rolled a </math>1<math>, then </math>2<math>. Probability: </math>frac{1}{6^2} = frac{1}{36} | ||
| + | 3. She rolled a <math>2</math>, then <math>1</math>. Probability: <math>frac{1}{6^2} = frac{1}{36} | ||
| + | 4. She rolled a </math>3<math> at the beginning. Probability: </math>frac{1}{6} | ||
| + | |||
| + | Add them together to get <math>\boxed{textbf{(B)} frac{49}{216}}</math> | ||
Revision as of 19:56, 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: 
1
2
frac{1}{6^2} = frac{1}{36}
3. She rolled a 
, then . Probability: 
3
frac{1}{6}
Add them together to get 
