In a random experiment,events $A$ and $B$ are such that $P(A) = \frac{1}{4}$,$P(A \mid B) = \frac{1}{2}$,and $P(B \mid A) = \frac{2}{3}$. Find $P(B)$.

For two events $A$ and $B$,$P(B) \neq 0$ and $P(A \mid B) = 1$,then . . . . . . .

One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

$A$ biased die is tossed and the respective probabilities for various faces to turn up are given below:

$Face$	$1$	$2$	$3$	$4$	$5$	$6$
$P(F)$	$0.1$	$0.24$	$0.19$	$0.18$	$0.15$	$0.14$

If an even face has turned up,then the probability that it is face $2$ or face $4$ is:

One card is drawn at random from a well-shuffled deck of $52$ cards. In which of the following cases are the events $E$ and $F$ independent?
$E:$ 'the card drawn is a spade'
$F:$ 'the card drawn is an ace'

$A$ and $B$ are two events such that $P(A) \neq 0$. Find $P(B | A)$ if $A \cap B = \phi$.