To find the probability that an integer selected at random from those between 20 and 100 inclusive is a multiple of 15, we first need to count the number of multiples of 15 in that range and then divide it by the total number of integers in that range.

Step 1: Find the number of multiples of 15 between 20 and 100.

The first multiple of 15 in that range is 15 itself. The last multiple of 15 in that range is 90.

So, we need to count how many multiples of 15 are there between 15 and 90.

Using the formula for counting multiples in a range:

Number of multiples = (Last multiple - First multiple) / Common multiple

Number of multiples = (90 - 15) / 15 = 75 / 15 = 5

There are 5 multiples of 15 between 20 and 100.

Step 2: Find the total number of integers between 20 and 100.

To find the total number of integers in that range, we subtract the lower bound (20) from the upper bound (100) and add 1.

Total number of integers = 100 - 20 + 1 = 81

Now, we can calculate the probability:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

Probability = (Number of multiples of 15) / (Total number of integers) = 5 / 81

So, the probability that an integer selected at random from those between 20 and 100 inclusive is a multiple of 15 is 5/81.