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?

Answer 1

`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`.
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`