Question

If a two digit number is selected at random, then what is the probability that it will be a multiple of '3' and not a multiple of '5'?

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is B

There is a total of 90 two digit numbers. Every third number will be divisible by '3'. Therefore, there are 30 of those numbers that are divisible by '3'.

Of these 30 numbers, the numbers that are divisible by '5' are those that are multiples of '15'. i.e. numbers that are divisible by both '3' and '5'.
There are 6 such numbers -- 15,30,45,60,75 and 90.

We need to find out numbers that are divisible by '3' and not by '5', which will be:
30 − 6 = 24.

24 out of the 90 numbers are divisible by '3' and not by '5'.

The required probability is, therefore, $\frac{4}{15}$.