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The probability that a person will get an electric contact is 2 5 and the probability that he will not get plumbing contract is 4 7 . If the probability of getting at least one contract is 2 3 , what is the probability that he will get both. Select the correct answer from above options

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Correct Answer - 17 105 17 Let E 1 = E event of getting an electrification contract, and E 2 E = event of getting a plumbing contract. Then, P ( E 1 ) = 2 5 , P ( not E 2 ) = 4 7 ⇒ P ( E 2 ) = ( 1 − 4 7 ) = 3 7 . P And, P ( E 1 ∪ E 2 ) = P ( E 1 or E 2 ) = 2 3 . P ∴ ∴ required probability = P ( E 1 ∩ E 2 ) = = P ( E 1 ) + P ( E 2 ) − P ( E 1 ∪ E 2 ) . =

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