Question

Spinners $A$ and $B$ are spun. On each spinner, the arrow is equally likely to land on each number. What is the probability that the product of the two spinners' numbers is even?

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{1}{2}$

$\dfrac{2}{3}$

$\dfrac{3}{4}$

Answer: D

Concepts:basic probability complementary probability parity

Difficulty rating: 1290

Solution:

For the product to be even, then at least one of the spinners must land on an even number.

We can use complementary counting and calculate the probability of both spinners landing on odds.

This happens with a probability of $\dfrac{1}{2} \cdot \dfrac{2}{3} = \dfrac{1}{3}.$

Then the probability of landing on at least one even is $1 - \dfrac{1}{3} = \dfrac{2}{3}.$

Thus, D is the correct answer.

2004 AMC 8 Problem 21

Answer: D

Difficulty rating: 1290

Solution:

Problem 21 in Other Years