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?

1 Answer
Nov 3, 2015

19/45, The procedure is explained below.

Explanation:

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