Question

What is the probability that, if a number is randomly chosen from any $31$ consecutive natural numbers, it is divisible by $5$?

• A. $\frac{6}{31}$
• B. $\frac{7}{31}$
• C. $\frac{6}{31}$ or $\frac{7}{31}$
• D. None of these

Answer 1

Answer: (C)

$\frac{6}{31}$ or $\frac{7}{31}$

The sample space is $31$ consecutive natural numbers.

However, there are two cases,

1. When the first number is a multiple of $5$:

Here, there will be $7$ numbers, divisible by $5$ and so probability becomes $\frac{7}{31}$

2. When the first number is not a multiple of $5$:

In this case, there only are $6$ multiples of $5$ and hence the probability becomes $\frac{6}{31}$

So, the correct answer is option C.