The odds in favour of drawing a king from a pack of $52$ playing cards is

In an entrance test that is graded on the basis of two examinations,the probability of a randomly chosen student passing the first examination is $0.8$ and the probability of passing the second examination is $0.7$. The probability of passing at least one of them is $0.95$. What is the probability of passing both?

Given $P(A) = \frac{3}{5}$ and $P(B) = \frac{1}{5}$. Find $P(A \text{ or } B)$,if $A$ and $B$ are mutually exclusive events.

If $P(A) = 0.4$,$P(B) = x$,$P(A \cup B) = 0.7$ and the events $A$ and $B$ are independent,then $x =$

Fill in the blanks in the following table:

$P(A)$	$P(B)$	$P(A \cap B)$	$P(A \cup B)$
$0.5$	$0.35$	$.........$	$0.7$

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: