Video Explanation

Text Explanation

First we need to determine how many numbers there are between 42 and 92 (including 42 and 92). Luckily, there is a formula for this:

There are 51 integers total between 42 and 92 inclusive. Now we just need to know how many odd and even numbers there are. Because we have even numbers on both sides of the range, we're going to have one more even number than we'll have odd numbers. If we started with an even and ended with an odd, or started with an odd and ended with an even, we'd have an equal number of odd and even numbers. To see why we have one more even in this case, let's look at a smaller range:

Range: 2 - 10

2, 3, 4, 5, 6, 7, 8, 9, 10

Even: 5

Odd: 4

Range: 38 - 48

38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48

Even: 6

Odd: 5

We start with an even number and then there's an odd, then even, then odd, and so forth. So for every even there's an odd, making them the same quantity all the way up until the last number, where we add one extra even number.

That means we'll always have one extra even number in a range that begins and ends with an even number. And we'll always have one extra odd number when the set begins and ends with odd numbers.

Another way to think about it is if we had 42 to 91. We'd have 50 integers. 25 even and 25 odd. We actually go to 92, so it's 26 even and 25 odd. Now we're ready to solve the problem. Column A is the probability that x is odd, so that's the number of odd numbers divided 

by the total amount of numbers: . Next Column B which is the probability that x is even. There are 26 even numbers, so it's . Column B is larger, so the answer is (B).