The probability that A hits a target is 1/3 and the probability that B hits it is 2/5 . -Maths 9th

The probability that A hits a target is 1/3 and the probability that B hits it is 2/5 . -Maths 9th
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1 Answer

Answer :

(b) \(rac{3}{5}\)Let A : Event that A hits the target B : Event that B hits the target Given,P(A) = \(rac{1}{3}\) ⇒ P(A not hitting the target) = P(\(\bar{A}\)) = 1 - \(rac{1}{3}\) = \(rac{2}{3}\)P(B) = \(rac{2}{5}\) ⇒ P(B not hitting the target) = P(\(\bar{B}\)) = 1 - \(rac{2}{5}\) = \(rac{3}{5}\)∴ P(Target is hit) = P(A hits) × P(B does not hit) + P(A does not hit) × P(B hits) + P(A hits) × P(B hits)= P(A) x P(\(\bar{A}\)) + P(\(\bar{A}\)) x P(B) + P(A) x P(B)= \(rac{1}{3}\)x \(rac{3}{5}\) + \(rac{2}{3}\)x \(rac{2}{5}\) + \(rac{1}{3}\) x \(rac{2}{5}\) = \(rac{3}{15}\) + \(rac{4}{15}\) + \(rac{2}{15}\) = \(rac{9}{15}\) = \(rac{3}{5}\).
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