2016 AMC 8 Problems/Problem 13
Contents
Problem
Two different numbers are randomly selected from the set and multiplied together. What is the probability that the product is ?
Solutions
Solution 1
1. Identify the total number of ways to select two different numbers from the set:
The set has 6 elements. The number of ways to choose 2 different numbers from 6 is given by the combination formula: .
2. Identify the favorable outcomes:
For the product to be zero, one of the chosen numbers must be zero. The set contains one zero (0). To have a product of zero, we need to choose 0 and any other number from the remaining five numbers .
The number of ways to choose 0 and one other number from the remaining five is 5.
3. Calculate the probability:
The probability is the number of favorable outcomes divided by the total number of outcomes: .
Thus, the probability that the product is is
~GeometryMystery
Solution 2 (Complementary Counting)
Because the only way the product of the two numbers is is if one of the numbers we choose is we calculate the probability of NOT choosing a We get Therefore our answer is
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Video Solution by OmegaLearn
https://youtu.be/6xNkyDgIhEE?t=357
~ pi_is_3.14
Video Solution
~savannahsolver
See Also
2016 AMC 8 (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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.