Most of you got it.

BMAD made a close estimate of the probability, which is actually just slightly greater than 60% to be co-prime.

I'm marking her answer, therefore.

Just for fun, I programmed up a little script. Using a suitable underlying GMP library for Euler's totient function, it checked up to 10 million in 13 seconds, with a result of 60.793% distinct pairs relatively prime.