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

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 $K=$ . . . . . . .

Fill in the blanks in the following table:

$P(A)$	$P(B)$	$P(A \cap B)$	$P(A \cup B)$
$\frac{1}{3}$	$\frac{1}{5}$	$\frac{1}{15}$	$........$

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:

The probability that a student will succeed in the $IIT$ entrance test is $0.2$ and the probability that he will succeed in the Roorkee entrance test is $0.5$. If the probability that he will be successful at both places is $0.3$,then the probability that he does not succeed at either place is:

The probability of an event happening is the square of the probability of a second event,but the odds against the first are the cube of the odds against the second. The probabilities of the events are: