Problem:
Each spinner is divided into equal parts. The results obtained from spinning the two spinners are multiplied. What is the probability that this product is an even number?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The only way to get an odd number for the product of two numbers is to multiply an odd number times an odd number. This happens if one spins on the first spinner chances out of and on the second spinner chance out of . Thus, the probability of an odd product is =. If one does not get an odd product, then the product is even. Hence the probability of an even product is =.
The sample space of pairs to be multiplied is:
Successful pairs are marked. The probability is .
Use a tree diagram:
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Thus the probability that the product is even is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions