Question

A bag contains $30$ balls numbered from $1$to $30$, one ball is drawn randomly. The probability that the number on the ball is multiple of $5$ or $7$ is

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $\frac{1}{4}$

Answer 1

The correct option is B

$\frac{1}{3}$

Explanation for the correct option:

Probability of choosing multiple 5 or 7:

Given, total number of ball in a bag having numbering $1,2,3,......30$ are $30$

Total number of ball in a bag having numbering multiple of $5=5,10,15,20,25,30$ are $6$.

Probability that the ball drawn from the bag which is multiple of $5$ is $\frac{6}{30}=\frac{1}{5}$

Similarly, Total number of ball in a bag which is multiple of $7=7,14,21,28$.

Probability that the ball drawn from the bag which is multiple of $7$is $\frac{4}{30}$

Now, The probability that the number on the ball is multiple of $5$ or $7$ is

$$\begin{gathered} \frac{1}{5}+\frac{4}{30} \\ =\frac{6+4}{30} \\ =\frac{1}{3} \end{gathered}$$

Therefore, The probability that the number on the ball is multiple of $5$ or $7$ is $\frac{1}{3}$

Hence, correct answer is option $\left(B\right)$.