Question

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?

पर्याय

• `16/45`

• `13/45`

• `14/45`

• `15/72`

Answer 1

`14/45`

Explanation:

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)

= `1-5/9=4/9`

Also, P(A∪B) = `4/5`

∴ Required probability, P (A∩B)
= P(A) + P(B) - P(A∪B)

= `2/3+4/9-4/5`

= `(30+20-36)/45=14/45`