NIMCET 2018 Question Paper with solutions

Given that , P (A ∪ B) = $\frac{5}{6}$ , P (A ∩ B) = $\frac{1}{3}$ and P (B) = $\frac{1}{2}$
P (A u B) = P (A) + P (B) - P (A ∩ B)
⇒ $\frac{5}{6}$ = P (A) + $\frac{1}{2}-\frac{1}{3}$
⇒ P (A) = $\frac{5}{6}+\frac{1}{3}-\frac{1}{2}$
= $\frac{5+2-3}{6}$
⇒ P (A) = $\frac{4}{6}$ = $\frac{2}{3}$
P (A) . P (B) = $\frac{2}{3}\times \frac{1}{2}$ = $\frac{1}{3}$ = P (A ∩ B)
∴ A and B are independent events