What is the probability that a positive integer selected at random from the set of positive integer not exceeding 100 is divisible by either 2 or 5 ? 

Calculation

We need to find the probability that a positive integer, selected randomly from 1 to 100 is divisible by either 2 or 5.

First, find the total number of positive integers from 1 to 100, which is 100.

Divisible by 2:

Every second number is divisible by 2, so there are 100 / 2 = 50 such numbers.

Divisible by 5:

Every fifth number is divisible by 5, so there are 100 / 5 = 20 such numbers.

There is an intersection between these two sets of numbers, namely, those numbers which are divisible by both 2 and 5 (that is, numbers divisible by 10). To avoid counting these twice, we need to subtract these from the total.

Divisible by 10 (both 2 and 5):

Every tenth number is divisible by 10, so there are 100 / 10 = 10 such numbers.

So, numbers that are divisible by either 2 or 5 are 50 (divisible by 2) + 20 (divisible by 5) - 10 (divisible by both) = 60.

Now, the probability of a number randomly picked from 1 to 100 being divisible by either 2 or 5 is 60/100 = 3/5.

Hence, the correct answer is option 2) 3/5.