Difference between revisions of "2016 AMC 8 Problems/Problem 13"
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There are a total of <math>30</math> possibilities, because the numbers are different. We want <math>0</math> to be the product so one of the numbers is <math>0</math>. There are <math>5</math> possibilities where <math>0</math> is chosen for the first number and there are <math>5</math> ways for <math>0</math> to be chosen as the second number. We seek <math>\boxed{\textbf{(D)} \, \frac{1}{3}}</math>. | There are a total of <math>30</math> possibilities, because the numbers are different. We want <math>0</math> to be the product so one of the numbers is <math>0</math>. There are <math>5</math> possibilities where <math>0</math> is chosen for the first number and there are <math>5</math> ways for <math>0</math> to be chosen as the second number. We seek <math>\boxed{\textbf{(D)} \, \frac{1}{3}}</math>. | ||
==Solution 3(Complementary Counting)== | ==Solution 3(Complementary Counting)== | ||
− | + | Because the only way the product is 0 is if a number we chose is 0 we calculate the probability of NOT choosing a 0. We get 5/6*4/5=2/3. 1-2/3=1/3 <math>\boxed{\textbf{(D)} \, \frac{1}{3}}</math> | |
{{AMC8 box|year=2016|num-b=12|num-a=14}} | {{AMC8 box|year=2016|num-b=12|num-a=14}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 13:01, 5 March 2020
Two different numbers are randomly selected from the set and multiplied together. What is the probability that the product is ?
Solution 1
The product can only be if one of the numbers is 0. Once we chose , there are ways we can chose the second number, or . There are ways we can chose numbers randomly, and that is . So, so the answer is .
Solution 2
There are a total of possibilities, because the numbers are different. We want to be the product so one of the numbers is . There are possibilities where is chosen for the first number and there are ways for to be chosen as the second number. We seek .
Solution 3(Complementary Counting)
Because the only way the product is 0 is if a number we chose is 0 we calculate the probability of NOT choosing a 0. We get 5/6*4/5=2/3. 1-2/3=1/3
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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All AJHSME/AMC 8 Problems and Solutions |
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