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

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

(i) P(A ∩ B) = P(A) + P(B) – P(A ∪ B)

= \(\frac{6}{11}\) + \(\frac{5}{11}\) – \(\frac{7}{11}\) = \(\frac{4}{11}\) 

 

(ii) 

\(P(\frac{A}{B})=\frac{P(A∩ B)}{P(B)})=\frac{\frac{4}{11}}{\frac{5}{11}}=\frac{4}{5}\)

 

(iii)

\(P(\frac{B}{A})=\frac{P(A∩ B)}{P(A)})=\frac{\frac{4}{11}}{\frac{6}{11}}=\frac{4}{6}=\frac{2}{3}\)