By picking a natural number randomly up-to 100.find the probability of the number being a perfect cube?
To find the probability of picking a perfect cube from the set of natural numbers up to 100, we need to find the total number of perfect cubes and divide it by the total number of natural numbers up to 100.
Total Number of Natural Numbers up to 100:
The natural numbers up to 100 are 1, 2, 3, 4, ..., 100. Therefore, there are 100 natural numbers up to 100.
Total Number of Perfect Cubes:
We need to find the number of perfect cubes that are within the range of 1 to 100. Perfect cubes are numbers that can be expressed as the cube of an integer.
1 is a perfect cube since 1^3 = 1.
2 is not a perfect cube.
3 is not a perfect cube.
4 is not a perfect cube.
5 is not a perfect cube.
6 is not a perfect cube.
...
8 is a perfect cube since 2^3 = 8.
9 is a perfect cube since 3^3 = 27.
10 is not a perfect cube.
...
By checking all integers, we can find that the perfect cubes within the range of 1 to 100 are 1^3, 2^3, 3^3, 4^3 = 1, 8, 27, 64. Therefore, there are 4 perfect cubes within this range.
Now, we can calculate the probability:
Probability of Picking a Perfect Cube = (Number of Perfect Cubes) / (Total Number of Natural Numbers)
Probability = 4 / 100
Simplifying the fraction, we have:
Probability = 1 / 25
So, the probability of picking a perfect cube from the set of natural numbers up to 100 is 1/25.
The following is a list of perfect Cubes
1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
4/100 = 1/25
1^=1
2^=8
3^=27
4^=64
4/100
=1/25