Question
Download Solution PDFThe 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:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
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
Last updated on Jul 17, 2025
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