Re: What is the probability of selecting a number that has exactly ...
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28 Jul 2021, 22:15
Finding the right answer to this question requires us to do 2 things :
1. Identify the numbers having exactly 3 factors
2. Finding the probability that if you pick any number randomly from the list, it belongs to the one in list #1
1. We all know that any integer is divisible by 1 and itself. That means 2 factors are bare minimum to any number. So, to identify the number with 3 factors, we just need to identify the numbers from the given list that have only one factor apart from 1 and itself.
Now, since all the numbers in the given list are perfect squares, the only integers that will have 1 extra factor in addition to 1 and itself would be the prime numbers. This is because composite numbers can be factorized into 2 or more integers, so we would never have 'only' 1 additional factor for composites.
For example,
for primes,
49 = 7^2 ; factors = {1,7,49}
25 = 5^2 ; factors = {1,5,25}
and for composites,
36 = 6^2 ; factors = {1,2,4,3,9,12,18,36}
2. since we have 4 numbers out of total 9 numbers as the squares of prime numbers ( 5^2 ,7^2 , 11^2 ,13^2 ) our probability would be 4/9.