Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.

QUESTION

# The probability that a contractor will get a plumbing contract is 2/3 and the probability that he will get an electric contract is 5/9. If the probability of getting at least one contract is 4/5, what is the probability that he will get both?

19/45, The procedure is explained below.

A is the event of getting a plumbing contract and p(A) = 2/3. B is the event of getting electrical contract and p(B) = 5/9. AuuB is the event of getting atleast one of them p(AuuB) = 4/5. By addition theorem of probability, P(AuuB) = p(A) + p(B) - p(AnnB). where p(AnnB) is the probability of getting both the contracts. P(AnnB) = p(A) + p(B) - P(AuuB). i.e. p(AnnB) =2/3 + 5/9 - 4/5 or (30 + 25 - 36)/45 p(AnnB) = 19/45