In probability questions, specifically OR problems (addition problems), the formula is:
P(A or B) = P(A) + P(B) - P(A AND B)
Why do we have to substract P(A AND B)?, I think we do that because P(A) and P(B) already include P(A AND B), right?
p(a) and p(b) both include p(a & b). so essentially when you want to write p(a or b), you mean p(only a)+p(only b)+p(a&b). ---1
where as, p(a)+p(b)= [p(only a)+ p(a&b)] + [p(only b)+p(a&b)]
hence you want to subtract p(a&b) from p(a)+p(b) to obtain equation #1.
Hope its clear. You should also try making a Venn diagram; that shall make this a bit more easier.