Question

The probability that a person will get an electric contract is $\frac{2}{5}$ and the probability that he will not get plumbing contract is $\frac{4}{7}$. If the probability of getting at least one contract is $\frac{2}{3}$, then the probability that he will get both is $\frac{17}{105}$.

• A. True
• B. False

Answer 1

The correct option is A True

Consider the following events:

A$=$ Person gets an electric contract,

B$=$ Person gets plumbing contract

We have,

$P\left(A\right)=\frac{2}{5},P\left(\overline{B}\right)=\frac{4}{7}$ and $P(A\cup B)=\frac{2}{3}$

Now,

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$\Rightarrow \frac{2}{3}=\frac{2}{5}+(1-\frac{4}{7})-P(A\cap B)$

$\Rightarrow P(A\cap B)=\frac{2}{5}+\frac{3}{7}-\frac{2}{3}=\frac{17}{105}$