Question

A number is chosen at random from the first ten natural numbers. The probability that number is odd and perfect square is

• A. $\frac{2}{9}$
• B. $\frac{2}{5}$
• C. $\frac{3}{7}$
• D. $\frac{1}{5}$

Answer 1

The correct option is D

$\frac{1}{5}$

Explanation for the correct option:

Step:1 Find the different ways of selecting a number from first ten natural numbers.

The different ways a number can be selected from first ten numbers is

$$\begin{gathered} =C_1^{10} \\ =10 \end{gathered}$$

Step: 2 Calculate the probability that the selected number is odd and perfect square.

The odd and perfect square numbers in between first ten natural numbers are $1$and $9$.

Hence, in between first ten natural numbers, there are only $2$ odd and perfect square numbers.

Therefore, the required probability

$$\begin{gathered} =\frac{2}{10} \\ =\frac{1}{5} \end{gathered}$$

Therefore, Option(D) is the correct answer.