this is a problem about condition probability . I am not asking for solutions (I have the solution already but dont understandt) but I hope to have some discussion about this problem

In a city, with equal number of male and female. 10% of male regarded as 'good-looking' while 10% of female regarded as 'good-looking'. They form couples randomly.

Given that a member of a couple is 'good-looking', find the probability that the other member is also'good-looking'

I was not able to do anything when I first saw this question. and I am now not able to understand when I see the solution.

I hope someone will teach me how to classify a problem, I want to have a clearer concept on probabilty. I don't want every time every old similiar questions make me feel like the new one ... it's painful

For example this one, the solution sets two events

M: good looking male

F: good looking female

then they go straight to a formula, - The required probability = P( L & G | L U G)

why?? why?? why isn't it P(G | L) + P(L | G)? I simply don't understand why I am wrong and how he determines the formula.

or why it can't be P(L & G | L) + P(L & G | G). Why??

I am in a big headache.

I understand the concept after reading the theories for many many times, but I now I don't really think I understand that