Question

What is the probability that a number selected at random from the set of numbers $\left\{1,2,3,\dots ,100\right\}$ is a perfect cube?

• A. $\frac{1}{25}$
• B. $\frac{2}{25}$
• C. $\frac{3}{25}$
• D. $\frac{4}{25}$

Answer 1

The correct option is A

$\frac{1}{25}$

Explanation of the correct option:

Finding the required probability:

Let $S$ be the set of all possible outcomes.

$$\begin{gathered} \Rightarrow S=\left\{1,2,3,\dots ,100\right\} \\ \Rightarrow n\left(S\right)=100 \end{gathered}$$

Let $A$ be the event of selecting a perfect cube from $S$.

$$\begin{gathered} \Rightarrow A=\left\{1,8,27,64\right\} \\ \Rightarrow n\left(A\right)=4 \end{gathered}$$

Therefore, the required probability $P\left(A\right)$ will be $\frac{n\left(A\right)}{n\left(S\right)}=\frac{4}{100}=\frac{1}{25}$.

Hence, the correct answer is option A.