Idle Questions of the Nicoll Kind...

... how far would you have to go between two stars in the galaxy (or, if that wouldn't suffice, the universe) to have a significant (say, >10%) chance of going through another star on the way (with "through" being "at some point you're within the photosphere")? Has anyone done this calculation (I'm sure SOMEONE has)? I suppose it's quite possible the answer is "go as far as you like, the chances will never exceed 1%" or something like that.