Question

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? express your answer as a common fractio

Answer 1

1/5

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