Question

Find the probability that a number selected at random from the set of 1,2,3,4,5, ….., 100 is a cube.

Answer 1

Hint: First of all, we should have an idea of definition of probability. we should know that the ratio of number of favourable outcomes to the total number of outcomes is equal to probability. The favourable outcome is to have a cube. So, the number of favourable outcomes is equal to the number of cubes between 1 and 100. The total number of outcomes is equal to the number of numbers from 1 to 100. By finding the ratio of number of cubes to number of numbers, we can get the probability of a number selected at random from the set 1,2,3,4,5, ….. 100.

Complete step-by-step answer:
Before solving the question, we should know that the ratio of number of favourable outcomes to the total number of outcomes is equal to probability.
So, to find the probability that a number selected at random from the set of 1,2,3,4,5, ….. 100 is a cube, we have to find the number of cubes from 1 to 100.
Let us consider the cubes possible. The cube of 1 is 1, 2 is 8, 3 is 27, 4 is 64, 5 is 125. Now since 125 is greater than 100, we get that cubes from 1 to 100 are 1, 8, 27 and 64.
So, the number of cubes from 1 to 100 are 4.
We know that the total number of numbers from 1 to 100 are 100.
It is clear that the favourable outcomes are to obtain a cube number and the total number of outcomes is to obtain a total number of numbers from 0 to 100.
It is clear that the number of favourable outcomes are equal to 4 and the total number of outcomes are equal to 100.
We know that the ratio of number of favourable outcomes to the total number of outcomes is equal to probability.
Probability that a number selected at random from the set of 1,2,3,4,5, ….. 100 is a cube is equal to $\dfrac{4}{100}$.
So, the probability that a number selected at random from the set of 1,2,3,4,5, ….. 100 is a cube $=\dfrac{1}{25}$

Note: We should remember that the probability of an event should be greater than (or) equal to zero and less than (or) equal to 1. Probability of an event is never greater than 1 and never less than zero. Students should be careful while finding the number of favourable outcomes in the question. We should write all the cubes below 100. We should not leave any cube number between 1 to 100 and we should not write extra numbers between 1 and 100.