The probabilities of three mutually exclusive events are $\frac{2}{3}$,$\frac{1}{4}$,and $\frac{1}{6}$. The statement is:

For two events $A$ and $B$,$P(A)=0.5$,$P(A \cup B)=0.6$ and $P(B)=K$ are given. If $A$ and $B$ are independent events,then $K=$ . . . . . . .

If $A$ and $B$ are mutually exclusive events,given that $P(A)=\frac{3}{5}$ and $P(B)=\frac{1}{5}$,then $P(A \text{ or } B)$ is

If two events $E_1$ and $E_2$ are such that $P(E_1 \cup E_2) = \frac{5}{8}$,$P(\bar{E}_1) = \frac{3}{4}$,and $P(E_2) = \frac{1}{2}$,then $E_1$ and $E_2$ are:

If $A$ and $B$ are independent events such that odds in favour of $A$ is $2:3$ and odds against $B$ is $4:5$,then $P(A \cap B)=$

Three critics review a book. For the three critics,the odds in favour of the book are $2:5$,$3:4$,and $4:3$ respectively. The probability that the majority is in favour of the book is given by