Emily is playing a board game that has a spinner divided into equal sections numbered 1 to 18. The probability of the spinner landing on an even number or a multiple of 3 ?

Jun 27, 2017

$\frac{2}{3}$

Explanation:

We want to find the probability of landing on an even number or a multiple of 3, so we should use the addition rule for the union of two events:

$P \left(A \mathmr{and} B\right) = P \left(A\right) + P \left(B\right) - P \left(A \mathmr{and} B\right)$

Let's make

• A = the probability of landing on an even number, and
• B = the probability of landing on a multiple of 3

What is P(A) (the probability of landing on an even number? 2, 4, 6, 8, 10, 12, 14, 16, and 18 are all even, so P(A) is $\frac{9}{18}$.

What is P(B) (the probability of landing on a multiple of 3? 3, 6, 9, 12, 15, and 18 are multiples of 3, so P(B) is $\frac{6}{18}$.

What is P(A and B) (the probability of landing on an even number that's also a multiple of 3)? 6, 12, and 18 are all even AND multiples of 3. So P(A and B) is $\frac{3}{18}$.

Now we can plug our values into the equation!

$P \left(A \mathmr{and} B\right) = P \left(A\right) + P \left(B\right) - P \left(A \mathmr{and} B\right)$

$P \left(A \mathmr{and} B\right) = \frac{9}{18} + \frac{6}{18} - \frac{3}{18}$

$P \left(A \mathmr{and} B\right) = \frac{12}{18}$

$P \left(A \mathmr{and} B\right) = \frac{2}{3}$