SOLUTION: A can solve 90% of the problems given in a book and B solve 70%. What is the probability that at least one of them will solve a problem selected at random from the book?

Question 658994: A can solve 90% of the problems given in a book and B solve 70%. What is the probability that at least one of them will solve a problem selected at random from the book?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
probability that A will solve a problem is .9
probability that B will solve a problem is .7
probability that both A and B will solve the problem is .9*.7 = .63
p (A or B) solve the problem is equal to p(A) + p(B) - p(A intersect B)
since the probability that each will solve the problem is independent of each other, this formula should apply and you will be p(A or B) = .9 + .7 - .63 = 1.6 - .63 = .97
the principal behind subtracting p(A intersect B) is to avoid it being double counted because p(A) includes p(A intersect B) and p(B) includes p(A intersect B) so if it wasn't subtracted, it would be counted twice.
note also that p(A) + p(B) by itself would be greater than 1 which can't be because the total probability always has to be less than or equal to 1.

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