Five balls are numbered 1 through 5 and placed in a bowl. Josh will randomly choose a ball from the bowl, look at its number and then put it back into the bowl. Then Josh will again randomly choose a ball from the bowl and look at its number. What is the probability that the product of the two numbers will be even and greater than 10

Each of the 5 balls has 5 possible combinations, as each one (1 - 5) can be paired with any of the 5. Therefore, the total number of combinations is 25.

For the product to be even, one of the balls has to be a 2 or 4. However, 2 multiplied by any number 1 - 5 is not greater than 10, so 2 is not an option. This means one of the balls has to be a 4.

There are only 3 numbers of 1 - 5 that, when multiplied by 4, are greater than 10. These are 3, 4, and 5.

This means that there are 5 combinations that work:

3 × 4 = 12

4 × 3 = 12

4 × 4 = 16

4 × 5 = 20

5 × 4 = 20

This means that 5 out of 25 combinations produce a result that is both even and greater than 10.

5/25 is then simplified to 1/5