1991 AJHSME Problems/Problem 22

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Problem

Each spinner is divided into $3$ equal parts. The results obtained from spinning the two spinners are multiplied. What is the probability that this product is an even number?

$\text{(A)}\ \frac{1}{3} \qquad \text{(B)}\ \frac{1}{2} \qquad \text{(C)}\ \frac{2}{3} \qquad \text{(D)}\ \frac{7}{9} \qquad \...$

Solution

Instead of computing this probability directly, we can find the probability that the product is odd, and subtract that from $1$ .

The product of two integers is odd if and only if each of the two integers is odd. The probability the first spinner yields an odd number is $2/3$ and the probability the second spinner yields an odd number is $1/3$ , so the probability both yield an odd number is $(2/3)(1/3)=2/9$ .

The desired probability is thus $1-2/9=7/9\rightarrow \boxed{\text{D}}$ .

1991 AJHSME (Problems • Resources)
Preceded by Problem 21	Followed by Problem 23
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1991 AJHSME Problems/Problem 22

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