Find $P(E | F)$ when two coins are tossed once,where $E$ is the event that a tail appears on one coin,and $F$ is the event that one coin shows a head.

An unbiased die is thrown twice. Let the event $A$ be 'odd number on the first throw' and $B$ the event 'odd number on the second throw'. Check the independence of the events $A$ and $B$.

From a lot containing $n$ good and $m$ bad articles,if $2$ articles are picked at random in succession without replacement,then the probability that the second article picked is bad is

$A$ random variable $X$ has the following probability distribution:

$X$	$0$	$1$	$2$	$3$	$4$
$P(X)$	$k$	$2k$	$4k$	$2k$	$k$

Then the value of $P(1 \le X < 4 | X \le 2) =$ ?

$A$ family has $3$ children. The probability that all the three children are girls,given that at least one of them is a girl is:

For two events $A$ and $B$,if $P(A) = P\left( \frac{A}{B} \right) = \frac{1}{4}$ and $P\left( \frac{B}{A} \right) = \frac{1}{2},$ then: