The probability that a contractor gets a plumbing contract is 2 / 3 and the probability that he will not get an electric contract is 5 / 9. If the probability of getting at least one contract is 4 / 5, then the probability that he will get both the contracts is:

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SSC CGL Tier-II ( JSO ) 2016 Official Paper ( Held On : 2 Dec 2016 )
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  1. 13 / 45
  2. 14 / 45
  3. 16 / 45
  4. 17 / 45

Answer (Detailed Solution Below)

Option 2 : 14 / 45
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Detailed Solution

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Given

The probability of getting plumbing contract = P(A) = 2/3

Probability of getting not electric contract P(B̅) = 5/9

Probability of getting atleast one contract P(A U B) = 4/5

Calculation

The probability of not getting electric contract = 1 - P(B̅)

⇒ = 1- 5/9 = 4/9

Probability of getting both the contracts P(A ∩ B) = P(A) + P(B) - P(A U B)

⇒ P(A ∩ B) = 2/3 + 4/9 - 4/5

⇒ (90 + 60 - 108)/135

∴ The probability that he will get both the contracts P(A ∩ B) is 14/45

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