Ten balls
Ten balls numbered from one to ten are inside a bag. Mia reaches in the bag and removes a ball. Jolène reaches in the bag and removes another ball. What is the probability that the sum of the numbers on the balls is even? Given that the answer can be expressed as a/b ( a and b are relatively prime), what is ?
The answer is 13.
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1 solution
The only ways for the sum to be even is if both the girls pick either even- or odd- numbered balls. Since there are the same number of even- and odd-numbered balls initially in the bag, whichever parity of ball MIa chooses, there will be 4 of the 9 balls remaining with the same parity that Jolene could remove from the bag. Thus the desired probability is 4 / 9 , giving us a + b = 4 + 9 = 1 3 .