A machine manufactured by a firm consists of two parts A and B. But of 100 A’s manufactured, -Maths 9th

A machine manufactured by a firm consists of two parts A and B. But of 100 A’s manufactured, -Maths 9th
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Answer :

Let E = {part A is defective}, F = {part B is defective}.Then, P (E) = \(rac{9}{100}\), P(F) = \(rac{5}{100}\)∴ P(\(\bar{E}\)) = 1 - \(rac{9}{100}\) = \(rac{91}{100}\) and   P(\(\bar{F}\)) = 1 - \(rac{5}{100}\) = \(rac{95}{100}\)Since E and F are independent, therefore, \(\bar{E}\) and \(\bar{F}\) and are also independent.Now P (none is defective) = P(\(\bar{E}\)) . P(\(\bar{F}\)) = \(rac{91}{100}\) x \(rac{95}{100}\)= 0.91 x 0.95 = 0.8645 = 0.86 to 2 d.p.
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