Difference between revisions of "2007 AMC 12B Problems/Problem 13"
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− | ==Problem | + | == Problem == |
A traffic light runs repeatedly through the following cycle: green for <math>30</math> seconds, then yellow for <math>3</math> seconds, and then red for <math>30</math> seconds. Leah picks a random three-second time interval to watch the light. What is the probability that the color changes while she is watching? | A traffic light runs repeatedly through the following cycle: green for <math>30</math> seconds, then yellow for <math>3</math> seconds, and then red for <math>30</math> seconds. Leah picks a random three-second time interval to watch the light. What is the probability that the color changes while she is watching? | ||
− | <math>\mathrm {(A)} \frac{1}{63} | + | <math>\mathrm{(A)}\ \frac{1}{63} \qquad \mathrm{(B)}\ \frac{1}{21} \qquad \mathrm{(C)}\ \frac{1}{10} \qquad \mathrm{(D)}\ \frac{1}{7} \qquad \mathrm{(E)}\ \frac{1}{3}</math> |
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+ | == Solution == | ||
The traffic light runs through a <math>63</math> second cycle. | The traffic light runs through a <math>63</math> second cycle. | ||
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<math>\frac{9}{63} = \frac{1}{7} \Rightarrow \mathrm{(D)}</math> | <math>\frac{9}{63} = \frac{1}{7} \Rightarrow \mathrm{(D)}</math> | ||
− | ==See Also== | + | == See Also == |
{{AMC12 box|year=2007|ab=B|num-b=12|num-a=14}} | {{AMC12 box|year=2007|ab=B|num-b=12|num-a=14}} | ||
[[Category:Introductory Combinatorics Problems]] | [[Category:Introductory Combinatorics Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 01:03, 19 October 2020
Problem
A traffic light runs repeatedly through the following cycle: green for seconds, then yellow for
seconds, and then red for
seconds. Leah picks a random three-second time interval to watch the light. What is the probability that the color changes while she is watching?
Solution
The traffic light runs through a second cycle.
Letting reference the moment it turns green, the light changes at three different times:
,
, and
This means that the light will change if the beginning of Leah's interval lies in
,
or
This gives a total of seconds out of
See Also
2007 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
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 |
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