something about probability

Those days I read a book, Statistic Reasoning, actually is about statistic with several notation of probability. From the character it can divide into two kinds of event:
Event 1,
Independent event
Dependent event
Event 2,
Non-overlapping event
Overlapping event
Take an example of overlapping event, as if, there are 20 people, and

	men	women
USA	2	6
French	4	8

 
however, what the propability of a person who is either French or a woman?
answer: form this question, we can notice that all of woman is included and all of french is included, thus, we can have:
included: (6(USA women)+8(French women))+4(French men)
not included:2(USA men)
so, the answer is:18/20