The probability that a person will get an electric contract is `2/5` and the probability that they will not get plumbing contracts `4/7dot` if the probability of getting at least one contract is `2/3` , what is the probability that he will get both?

Explanation

Let,`A =` Person gets an electric contract

`B =` Person gets plumbing contract

`P(A)=2/5​,P(B')=4/7`​ and `P(A∪B)=2/3`
​

Now, `P(A∪B)=P(A)+P(B)−P(A∩B)`

`2/3​=2/5​+(1−4/7​)−P(A∩B)`


`P(A∩B)=17/105`​