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2016 AMC 10B Problem 12

Problem 12 of 25IntermediateNumber TheoryCounting & Probability

Two different numbers are selected at random from {1,2,3,4,5}\{1, 2, 3, 4, 5\} and multiplied together. What is the probability that the product is even?

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Solution

The product is odd if and only if both numbers are odd. There are (32)=3\binom 32=3 ways to do this out of a possible (52)=10\binom 52=10 ways. This makes the probability of it being odd equal to 310=0.3.\frac 3{10} = 0.3. This means the probability it is even is 10.3=0.7.1-0.3=0.7. Thus, the correct answer is D .

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Concepts: basic probability · complementary counting · parity

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.