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.

$A$ cubical die with faces marked $1, 2, 3, ..., 6$ is tossed such that the probability of throwing the number $t$ is proportional to $t^2$. The probability that the number $5$ has appeared,given that the number turned up is not even,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:

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'

If $2 P(A) = P(B) = \frac{5}{13}$ and $P(A \mid B) = \frac{2}{5}$,then $P(A \cup B) = $ . . . . . . .

If $P(A)=0.8, P(B)=0.5$ and $P(B | A)=0.4,$ find $P(A | B).$