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 floor(40/6) = 6 integers in the range that are divisible by 6.

There are floor(40/8) = 5) integers in the range that are divisible by 8.

One of those, 24, is divisible by both 6 and 8, so is counted twice. Then the number of unique numbers 1 to 40 that are divisible by 6 or 8 is ...

6 + 5 - 1 = 10

The probability of selecting one of those at random is ...

10/40 = 1/4