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 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.
+1084 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?
:)
