2016 AMC 10B Problem 12

Question

Two different numbers are selected at random from

\{1, 2, 3, 4, 5\}

and multiplied together. What is the probability that the product is even?

\ 0.2

\ 0.4

\ 0.5

\ 0.7

\ 0.8

Count the odd-product pairs instead

There are

\binom32

odd pairs out of

\binom52

pairs

The product is odd if and only if both numbers are odd. There are

\binom 32=3

ways to do this out of a possible

\binom 52=10

ways. This makes the probability of it being odd equal to

\frac 3{10} = 0.3.

This means the probability it is even is

1-0.3=0.7.

Thus, the correct answer is D .

Problem 12 in other years