# A random positive integer is chosen from numbers 1-100. What is the probability that it is not divisible by 5 but divisible by 2?

## Expert Answers An integer is picked from those that lie in the range 1-100. The total number of integers from which a choice can be made is 100.

The number of integers divisible by 5 in this range is 20 and the number of integers divisible by 2 in this range is 50. Also, there are 10 numbers that are divisible both by 2 as well as 5. The numbers not divisible by 5 but divisible by 2 is 40.

This gives P(2) = 50/100 = 0.5, P(5) = 20/100 = 0.2 and P(2&5) = 10/100 = 0.1

A random number not divisible by 5 has a probability 0.8

The probability P(n5&2) = P(n5) + P(2) - P(n5&2) = 0.8 + 0.5 - 0.4 = 0.9

The probability of a number being divisible by 2 but not by 5 is 0.9

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