It depends on what you mean by published.
Today more than ever there is a continuum of publishing options. What used to be called self-published is often referred to as independently published now. (This can get confusing because there are also independent publishers--a whole other thing--more on this in a moment). If you choose to publish independently, you no longer have to use an expensive vanity press or bang your head against the brick walls of the chain bookstores, which tend not to carry so-called indie titles. In fact, you don't have to print your book at all. Authors like Karen McQuestion have hit the publishing jackpot after self-publishing their novels on Kindle, promoting on the Kindle boards, seeing their sales figures rise, and ultimately receiving offers from agents, publishers, and in some cases, Amazon's own publishing arm, Encore.
So any novel can be published today by the above criterion.
If what you mean is traditionally published, there are at least three different paths.
There are the majors (Random House, HarperCollins, etc., which add up to the so-called Big 6, although imprints within these 6 bring the total to between 20 and 30 depending on what you write).
And then there are the well-established independents (Counterpoint, Overlook, Milkweed, Algonquin, Grey Wolf, Sourcebooks, Poisoned Pen, to name just a few).
Finally, there are ever more brand new, very small ("micro") presses cropping up. Four of these are Krill Press, Oak Tree Press, Echelon Press, and Wolfmont, but there are many others to check out.
If your work is good, falls within required word limits, and you have a good marketing sense and platform established by the time you begin submitting your novel, I'd say there is a much better-than-the-lottery chance that you can at least interest the publisher of one of the new, small presses in you and your work.
The majors will always be something of a lottery. In addition to an absolutely top drawer manuscript (ms), you have to get many people along the way to fall in love with your novel. First an agent, then other agents at that agency; then an editor; then everyone else at the publishing house, right up to the publisher him or herself, plus the marketing departments.
You have to have a project that hasn't been done recently or isn't forthcoming at the house, while simultaneously not being different or unusual enough that it would be hard to slot into a niche. You have to have enough of an identity that you are a good marketing bet. And then there's the intangible fact of that "falling in love" thing. We all know love is hard to find, and subjective. The requirement that 6 or more people fall in love with the same novel sets the bar so high that I'd say getting an offer from the majors is much, much less likely than not--and that's even if you're a stellar talent.
On the other hand, less than stellar stuff is published all the time--again because there's a certain capricious factor that comes of requiring so many stars to align.
My short answer is that if you're willing to entertain some of the brand new presses appearing on the scene, you should be able to get your novel published, provided it's good.
If your heart is set on the majors, you just might be better off buying that lottery ticket.
If you win, you can start your own publishing house ;)