Question

A number is chosen at random among the first $120$ natural numbers. The probability of the number chosen to be a multiple of $5$ or $15$ is:

• A. $\frac{1}{5}$
• B. $\frac{1}{8}$
• C. $\frac{1}{24}$
• D. $\frac{1}{6}$

Answer 1

The correct option is A

$\frac{1}{5}$

Explanation for the correct option:

Step: 1 Find out the ways a number can be chosen at random from the first $120$ natural numbers.

The ways a number can be chosen at random from the first $120$ numbers is

$$\begin{gathered} =C_1^{120} \\ =120 \end{gathered}$$

Step: 2 Find out the probability of the chosen number to be a multiple of $5$ or $15$.

The numbers in between $1$to $120$ that are multiple of $5$or $15$ are $[5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120]$.

Therefore, total numbers in between $1$to $120$ that are multiple of $5$or $15$ is $24$.

Therefore, the required probability is

$$\begin{gathered} =\frac{24}{120} \\ =\frac{1}{5} \end{gathered}$$

Therefore, Option (A) is the correct answer.