If you pick any two integers at random, what is that probability that they will be relatively prime? ("relatively prime" means that the two numbers share no divisors except 1)
Tell how you end up with the answer.
(In reply to
First steps.... by fwaff)
Except that you don't add the probabilities. The probability of A or B occuring is 1 - the probability of neither occuring. If A and B are independent (and I think they are for this problem), P(A or B) = 1 - (1 - P(A)) x (1 - P(B)). This gives the even more complicated formula of:
1 - (1 - 1/4) x (1 - 1/9) x (1 - 1/25) ... (1 - 1/n²)... for all prime n.
re: First steps....
