Choose an integer randomly from the set 1,2,3,...,99,100. Square it, then subtract 1. What is the probability that the resulting value is a prime number?

Guest Aug 30, 2020

#3**0 **

The answer is 1/100.

(it's correct)

Out of all the numbers 1-100, if you square 2 and subtract one, it gives you a prime. All the others don't work. I'm not too sure how this works, hopefully someone can explain.

Guest Aug 30, 2020

#5**+1 **

Instead of using words to think about it, let's use variables and numbers!

What the problem is asking is: For what numbers 1 - 100 is n^2 - 1 prime?

First, we need to know what n^2 - 1 is. This is (n-1)(n+1). (Difference of squares?)

We see that for it to be a prime number, n - 1 has to be 1. The only number that this works is 2.

So the answer is 1/100

Guest. Do you understand now?

:)

ilorty Aug 31, 2020