Question

Let the sample space consist of non-negative integers up to $50$, $X$ denote the numbers which are multiples of $3$ and $Y$ denote the odd numbers. Which of the following is/are correct?
(1) $P\left(X\right)=\frac{8}{25}$
(2) $P\left(Y\right)=\frac{1}{2}$
Select the correct answer using the code given below:

• A. $1$ only
• B. $2$ only
• C. Both $1$ and $2$
• D. Neither $1$ nor $2$

Answer 1

Answer: (C)

Both $1$ and $2$

Number of multiples of $3$ from $1$ to $50=16$

$\Rightarrow P\left(X\right)=\frac{16}{50}=\frac{8}{25}$

Number of odd numbers from $1$ to $50=25$

$\Rightarrow P\left(Y\right)=\frac{25}{50}=\frac{1}{2}$

Hence, both $1$ and $2$ are correct.