Explanation

Use both probability and number properties concepts in order to answer this question.

First, in order for two integers to produce an odd integer, the two starting integers must be odd. An odd times an odd equals an odd. An even times an odd, by contrast, produces an even, as does an even times an even.

Within the set of tiles, there are 50 even numbers (2, 4, 6, …, 100) and 50 odd numbers (1, 3, 5, …,99).

One randomly-chosen tile will have a \(\frac{50}{100}=\frac{1}{2}\) probability of being even, and a \(\frac{1}{2}\) probability of being odd.

The probability of choosing an odd tile first is \(\frac{1}{2}\) and the probability of choosing an odd tile second is also , so the probability of “first odd and second odd” is \(\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\).