The probability that a contractor will get a plumbing contractor is `2/3`. and the probability that he will not 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?
Let the probability of getting plumbing contract P(A) = `2/3`
and the probability of getting an electric contract P(B) = 1 - P (not getting electric contract)
Also, P(A∪B) = `4/5`
∴ Required probability, P (A∩B)
= P(A) + P(B) - P(A∪B)