Probability of Even vs. Odd SumsDate: 10/11/2000 at 17:32:15 From: Anonymous Subject: Probability of even vs. odd sums Hi Dr. Math, My second-grade son asked a question of his math teacher and was not satisfied with her answer. She taught the class that the sum of two even numbers will be even, the sum of two odd numbers will be even, and the sum of one odd and one even number will be odd. He asked her, since there are more ways to achieve an even sum, is it more likely that an addition problem will have an even answer? She said, "No, it depends on the addends." He understands that it depends on the specific problems he is given, but still feels that overall, addition problems are more likely to have even answers. Can you provide a reasonable explanation for him as to why this is true or not true? Thank you in advance Date: 10/12/2000 at 12:15:44 From: Doctor Anthony Subject: Re: Probability of even vs. odd sums You have to be a little careful here because you are dealing with infinite sets. However, if we are limited to the set of numbers 1 to 100, there are 50 even numbers and 50 odd numbers. We can choose 2 even numbers in 50 x 50 = 2500 ways We can choose 2 odd numbers in 50 x 50 = 2500 ways We can choose 1 odd and 1 even in 50 x 50 = 2500 ways We can choose 1 even and 1 odd in 50 x 50 = 2500 ways The sum of the two numbers is even on 2 x 2500 = 5000 occasions. The sum of the two numbers is odd on 2 x 2500 = 5000 occasions. So there is no bias in favor of an even sum. - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ |
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