Question

A number is selected at random from integers $1to100$. Find the probability that it is not a perfect cube.

Answer 1

Sample space $=\{1,2,3,4,5,\dots ,100\}$

Let $A$ be the event of getting a perfect cube

$A=\{1,8,27,64\}$

$n\left(A\right)=4$

Probability of getting a perfect perfect cube, $P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}$

$=\frac{4}{100}=\frac{1}{25}$

Let $B$ be the event of getting not a perfect cube.

Probability of getting not a perfect cube,$P\left(B\right)=1-P\left(A\right)$

$=1-\frac{1}{25}=\frac{25-1}{25}=\frac{24}{25}$