Question

Each of two boxes contains three chips numbered $1,$ $2,$ $3.$ A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even?

$\dfrac{1}{9}$

$\dfrac{2}{9}$

$\dfrac{4}{9}$

$\dfrac{1}{2}$

$\dfrac{5}{9}$

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Written solution:

The product is odd only when both chips are odd. Each box has two odd chips, $1$ and $3$ , out of three chips, so the probability of an odd product is $(\dfrac23)^2=\dfrac49$ .

The probability of an even product is the complement, $1-\dfrac49=\dfrac59$ .

Thus, E is the correct answer.

2015 AMC 8 Problem 7

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Problem 7 in Other Years