Question

An integer is chosen at random from the first 40 positive integers. What is the probability that the integer chosen is divisible by 6 or 8?

Answer 1

1/4

Explanation:

There are 40/8 = 5 integers in the range that are divisible by 8. There are floor(40/6) = 6 integers in the range that are divisible by 6. Of those sets of integers, one (24) is divisble by both numbers. So, altogether, there are 5+6-1 = 10 of the 40 integers that are divisible by 6 or 8.

If you choose an integer at random from the range 1–40, the probability is 10/40 = 1/4 that it will be divisible by 6 or 8.