Elvis had a twin brother (who died at birth).
Historically, approximately 1/125 of all births were fraternal twins and 1/300 were identical twins. The probability that Elvis was an identical twin is approximately . . .
5/11, or 45%.
Isn't it (1/300) / (1/125 + 1/300) = 5/17 ~ .29?
No, it's 5/11. See http://www.stat.columbia.edu/~gelman/book/ and go to the solutions to exercises in the second edition, Exercise 1.6.
Here's how I think of it:
In 3000 births, we would expect 3000/300 = 10 sets of identical twins. Roughly half of those we would expect to be boys. That's 5 sets of boy-boy identical twins.
In 3000 births, we would expect 3000/125 = 24 sets of fraternal twins. One fourth would be boy-boy, one-fourth would be girl-girl, one fourth would be boy-girl, and one fourth girl-boy. Therefore six sets would be boy-boy.
So, out of 3000 births, five out of eleven sets of boy-boy twins would be identical. Therefore the chances that Elvis was an identical twin is about 5/11.