2016 AMC 10B Problems/Problem 12
Problem
Two different numbers are selected at random from and multiplied together. What is the probability that the product is even?
Solution 1
The product will be even if at least one selected number is even, and odd if none are. Using complementary counting, the chance that both numbers are odd is , so the answer is
which is
.
An alternate way to finish:
Since it is odd if none are even, the probability is .
~Alternate solve by JH. L
Solution 2
There are cases to get an even number. Case 1:
and Case 2:
. Thus, to get an
, you get
. And to get
, you get
.
which is
and the answer is
.
Video Solution
https://youtu.be/tUpKpGmOwDQ - savannahsolver
https://youtu.be/IRyWOZQMTV8?t=933 - pi_is_3.14
See Also
2016 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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All AMC 10 Problems and Solutions |
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