**Question **: Events A and C are independent. If the probabilities relating A, B and C are P(A)=1/5, P(B)=1/6, P(AnC)=1/20, P(BUC)=3/8, then

(A) Events B and C are independent

(B) Events B and C mutually exclusive

(C) Events B and C bare neither independent nor mutually exclusive

(D) Events B and C are equiprobable

**Answer **: option (A)

**Solution **:

P(A n C) = P(A) P(C)

\Rightarrow \dfrac{1}{20}=\dfrac{1}{5}P\left( C\right) \Rightarrow p\left( C\right) =\dfrac{1}{4}now, \begin{aligned}\Rightarrow P\left( B\cup C\right) =\dfrac{1}{6}+\dfrac{1}{4}-P\left( B\cap C\right) \ \Rightarrow P\left( B\cap C\right) =\dfrac{3}{8}-\dfrac{1}{3}=\dfrac{1}{24}=P\left( B\right) P\left( C\right) \end{aligned}

Therefore, B and C are independent