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