JEE-Mains 2014 (26/30)

Probability Level 2

Let $A$ and $B$ be two events such that $P(\overline{A \cup B})=\frac{1}{6}$ , $P(A \cap B)=\frac{1}{4}$ and $P(\overline{A})=\frac{1}{4}$ , where $\overline{A}$ stands for the complement of the event $A$ . Then the events $A$ and $B$ are :

equally likely but not independent. mutually exclusive and independent. independent and equally likely. independent but not equally likely.