Question

A number is selected randomly from the first thirty natural numbers. What are the chances that it is a multiple of either 3 or 13?

• A. 13/30
• B. 2/5
• C. 3/5
• D. 17/30
• E. None of these

Answer 1

The correct option is B

2/5

The probability that the number is a multiple of 3 is $\frac{10}{30}$.

Similarly, the probability that the number is a multiple of 13 is $\frac{2}{30}$.

Neither 3 nor 13 has common multiples from 1 to 30.
Hence, these events are mutually exclusive events.
Therefore, chances that the selected number is a multiple of 3 or 13 is: $\frac{12}{30}$ = $\frac{2}{5}$