Question

A number is selected at random from $1$ to $50$. What is the probability that it is not a perfect cube?

Answer 1

The total number of outcomes are $50$.

Since, the perfect cubes from numbers $1$ to $50$ are $1,8$ and $27$.

Therefore, if a number is selected at random then the possible outcomes that it is not a perfect cube are

$2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,28,$
$29,30,31,32,33,34,35,36,37,38,39,$ $40,41,42,43,44,45,46,47,48,49,50$

which means the number of favourable outcome is $47$.

Therefore, probability $P$ that it is not a perfect cube is:

$P=\frac{47}{50}$

Hence, the probabilitythat it is not a perfect cube is $\frac{47}{50}$.