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counting and probability intermediate
Problem
Two different numbers are selected at random from and multiplied together. What is the probability that the product is even?
(A)
(B)
(C)
(D)
Solution
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 .
Final answer
D