By picking natural numbers randomly upto 100.Find the probability of number being a perfect cube?

http://www.jiskha.com/display.cgi?id=1490112196

To find the probability of a number being a perfect cube when picking natural numbers randomly up to 100, we need to determine the number of perfect cubes between 1 and 100.

A perfect cube is a number that can be expressed as the cube of an integer. For example, 1, 8, 27, 64, and so on, are perfect cubes.

To find all the perfect cubes between 1 and 100, we can calculate the cube root of the smallest perfect cube (1) and the largest perfect cube (100). The smallest perfect cube is 1^3 = 1, and the largest perfect cube is 4^3 = 64.

So, the perfect cubes between 1 and 100 are: 1, 8, 27, and 64.

Since there are 4 perfect cubes between 1 and 100, and there are 100 natural numbers to choose from, the probability of randomly picking a perfect cube is 4/100, which simplifies to 1/25.

Therefore, the probability of randomly picking a perfect cube when selecting natural numbers up to 100 is 1/25.