I’m a big fan of US agent Kristin Nelson’s blog, and one of the things I love is her transparency. If you look here and here, you can get a good idea of how many queries, samples, and full manuscripts get to the next stage at her agency. She is a successful agent with a strong web presence, so I imagine she gets more queries than the norm – but I also think she has the capacity to accept more books than a tiny agency. Therefore, I think the rate of these statistics gives a good general idea of how difficult it is to get an agent in the USA.
Getting an agent is not at all the same thing as getting published, but I think your chances of getting published with an agent are about 80% – more for someone of Kristin’s calibre. Which is a huge amount compared to the 1 in 10,000 shot of the average unpublished novel.