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##. A##uu##B is the event of getting atleast one of them p(A##uu##B) = ##4/5##. By addition theorem of probability, P(A##uu##B) = p(A) + p(B) – p(A##nn##B). where p(A##nn##B) is the probability of getting both the contracts. P(A##nn##B) = p(A) + p(B) – P(A##uu##B). i.e. p(A##nn##B) =##2/3## + ##5/9## – ##4/5## or ##(30 + 25 – 36)/45## p(A##nn##B) = ##19/45##