¶ 1987 AMC8 Problem 25
Problem:
Ten balls numbered to are in a jar. Jack reaches into the jar and randomly removes one of the balls. Then Jill reaches into the jar and randomly removes a different ball. The probability that the sum of the two numbers on the balls removed is even is
Answer Choices:
A.
B.
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D.
E.
Solution:
Since Jack and Jill cannot remove the same number, there are ways they can remove the two balls from the jar as shown by the unshaded squares on the grid. Those squares representing an even sum are labeled "". There are such squares - in each column (or row) since the two numbers must both be odd or both be even. The probability is .
There are ways to select the first number but only ways to select the second since it must have the same parity (both odd or both even) as the first. Thus the probability is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions