Question

If P(A) = $\frac{6}{11}$, P(B) = $\frac{5}{11}$ and P(A ∪ B) =$\frac{7}{11}$ , find
(i) P(A∩B)
(ii) P(A|B)
(iii) P(B|A)

Answer 1

If P(A) = $\frac{6}{11}$, P(B) = $\frac{5}{11}$ and P(A ∪ B) =$\frac{7}{11}$

To find

(i) P(A∩B) :

we know that

P(A∩B) = P(A)+P(B)-P(A ∪ B)


=
$\frac{6}{11} + \frac{5}{11} - \frac{7}{11} \\ \\ = \frac{6 + 5 - 7}{11} \\ \\ = \frac{4}{11}$
(ii) P(A|B) :

To find conditional probability

P(A|B) =P(A∩B)/P(B)

$= \frac{4}{11} \times \frac{11}{5} \\ \\ = \frac{4}{5}$

(ii) P(B|A) :

To find conditional probability

P(B|A) =P(A∩B)/P(A)

$= \frac{4}{11} \times \frac{11}{6} \\ \\ = \frac{4}{5}$