Lucky 13

I think luck can play a big role in how well musicians do in the industry. It definitely makes their journey to the top much, much easier.
One example would be people who have relatives in the music industry. It's just like having an older brother or sister growing up. They are the ones that experience everything first, so when it's your turn, you're able to ask questions and get help from them. And the term "popular by association" comes to mind. If your dad was a famous artist, and people liked him, they might be interested in seeing how you turned out. People are curious in that way sometimes. For instance, take the Cyrus family. Billy Ray is a country singer, well known for his #1 hit, "Achy Breaky Heart". Then his daughter, Miley, starts her own music career, and people are like, "Hey, that's Billy Ray's daughter!". And they check her stuff out, from curiosity.
Another example of some luck would be if you had started out in another industry, such as movies or television, before pursuing a music career. That way you are already well known, and don't have to struggle with getting popular. Take Hilary Duff, she was in television shows and movies before she began a music career. The public knew her well, so when she did start, it was easier to get her music out there because of her already established fan base.
Without much luck, but a good amount of talent, you can still be successful in the music industry. It usually just takes more time to work your way up there. My Chemical Romance comes to mind for me, since I've watched a DVD on them talking about how they began their journey. MCR had started out by writing songs and recording them in one of the member's attic. They took these songs and were able to get a record label, and recorded their first album. Their gave free song downloads through MySpace and PureVolume, so they could build up a fan base. And they performed at various venues, in the hopes of getting more attention. A couple years later, they sign with a new label, and that's when they really hit it off. Look at them now, all that work paid off.
It was quite hard to write this post, because I think most artists have a bit of both elements. Even though I used examples for luck and talent, each of them needed the other as well to get where they are now.

Or you could just be silly like me and say that every artist is lucky that they were able to sing so well in the first place! :)