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?
The probability is 1/20.
The answer is 1/100.
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.
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?