It is given that $A$ and $B$ are such that $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$. Then $P(B) = $?

If two unbiased dice are rolled simultaneously until a sum of the numbers appearing on these dice is either $7$ or $11$, then the probability that $7$ comes before $11$ is:

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.

$A$ and $B$ are two events such that $P(A) = 0.8$,$P(B) = 0.6$,and $P(A \cap B) = 0.5$. Then the value of $P(A/B)$ is:

If $A$ and $B$ are two events such that $A \subseteq B,$ then $P\left( \frac{B}{A} \right) = $

If $A$ and $B$ are two events such that $P(A \cap B) = 0.1$,and $P(A \mid B)$ and $P(B \mid A)$ are the roots of the equation $12x^2 - 7x + 1 = 0$,then the value of $\frac{P(\overline{A} \cup \overline{B})}{P(\overline{A} \cap \overline{B})}$ is: