Suppose a number from 1 to 100 is selected at random. what is the probability that a multiple of 4 or 5 is chosen?

the range 1-100 is 100 numbers, divide by 4 and 5 to find the number of multiples.
100/4 = 25
100/5 = 20

probability of choosing multiple of 4
25/100 = 1/4
probability of choosing multiple of 5
20/100 = 1/5

the probabilities are not mutually exclusive because there are duplicate numbers, (overlap) multiples of both 4 and 5 being counted twice. 5/100 = 1/20
20, 40, 60, 80, 100

when "or" is used, add the probabilities, subtract the duplicates.

1/4 + 15 - 1/20 =
5/20 + 4/20 - 1/20 = 8/20 = 2/5