A can solve 90% of the problems given in a book and B can solve 70%. What is the probability that at least one of them -Maths 9th

A can solve 90% of the problems given in a book and B can solve 70%. What is the probability that at least one of them -Maths 9th
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Answer :

Let E be the event that A solve the problem and F the event that B solves the problem.Then P(E) = \(rac{90}{100}\) = \(rac{9}{10}\), P(F) =\(rac{70}{100}\) = \(rac{7}{10}\),  P(\(\bar{E}\)) = 1 - \(rac{9}{10}\) = \(rac{1}{10}\),  P(\(\bar{F}\)) = 1 - \(rac{7}{10}\) = \(rac{3}{10}\)∴ Probability that no one solves the problem P(\(\bar{E}\)) . P(\(\bar{F}\)) = \(rac{1}{10}\)x \(rac{3}{10}\) = \(rac{3}{100}\).Hence, probability that at least one of them will solve a problem = 1 - \(rac{3}{100}\) = \(rac{97}{100}\) = 0.97.
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