Two of the numbers {1, 2, 3, ..., 100} are chosen at random. What is the probability that their sum is odd?
Two of the numbers {1, 2, 3, ..., 100} are chosen at random. What is the probability that their sum is odd?
To obtain an odd sum, requires one even number and one odd number.
If you have two even numbers, or two odd numbers, the sum will be even.
So pull one number. It can be anything, because the second number will determine whether the sum is odd or even.
Once you have your first number, if it's even you need to pull an odd number. All fifty of them are left.
if it's odd you need to pull an even number. All fifty of them are left.
So, there are 99 numbers left – remember, you've already pulled one out – and 50 of them are the one you want.
Your chance of getting one of the numbers to make an odd sum is 50/99
.
