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 either of contract is 4/5. What is the probability that he will get both?

Answer 1

Answer:

1/5

Step-by-step explanation:

This question makes use of the formula

P(A∪B) = P(A) + P(B) - P(A∩B)

Here the contractor can get either A (plumbing) or B(electric), but there's no such constraint, that he can get only one at a time. He can have both contracts at the same time, which is exactly what P(AUB) will give you.

so applying that formula, we have

4/5 = 2/3 + 5/9 - P(A∩B)

P(A∩B) = 1/5