I'm trying to find the probability that two randomly-selected letters from "average" text in a language will be the same.
For example, if my hypothetical language contains four letters which each occur on average with the following frequency:
A = 60% B = 25% C = 10% D = 5%
What is the probability that selecting any two letters from a representational text will be the same?
My intuition for solving this is first to find the chance that they're different, so the sum over the probabilities that a letter is chosen and then some other letter is chosen next, over each letter in the alphabet:
(0.6 * (1 - 0.6) + 0.25 * (1 - 0.25) + 0.1 * (1 - 0.1) + 0.05 * (1 - 0.05)) = 0.565
Then the chance that they are the same:
1 - 0.565 = 0.435
Is this reasoning sound? It seems like a very basic probability problem, but I always seem to be thinking about these things in the wrong way and would appreciate a sanity check (and any pointers to materials which would help me be more confident about this kind of thing in the future!)