Answer:
a.) 0.0402
b.) 0.00789
Step-by-step explanation:
In between the numbers 1 and 1012,
The number of perfect squares we have is 31, that is all numbers between 1 and 31 inclusive have their squares between the numbers 1 and 1012
The number of perfect cubes we have is 10, that is all numbers between 1 and 10 Inclusive have their perfect cube between the numbers 1 and 1012.
The number of perfect Fourth we have is 5, that is all numbers between 1 and 5 inclusive have their perfect fourth between the numbers 1 and 1012.
The number of perfect Sixth we have is 3, that is all numbers between 1 and 3 inclusive have their perfect sixth between the numbers 1 and 1012.
Hence,
a.) probability of choosing a perfect square = 31/1012
Probability of choosing a perfect cube = 10/1012
Probability of choosing a perfect square or a perfect cube = (31/1012) + (10/1012) - [(31/1012)*(10/1012)]
=41/1012 - 310/1024144
=0.0405 - 0.0003
=0.0402.
b.) Probability of choosing a perfect fourth or a perfect Sixth = (5/1012) + (3/1012) - [(5/1012)*(3/1012)]
= 8/1012 - 15/1024144
= 0.00789.
