If $A$ and $B$ are independent events with $P(A) = \frac{1}{3}$ and $P(B) = \frac{2}{7}$,then the value of $P\left(\frac{A}{B^C}\right)$ is

Consider the experiment of throwing a die. If a multiple of $3$ comes up,throw the die again,and if any other number comes,toss a coin. Find the conditional probability of the event 'the coin shows a tail',given that 'at least one die shows a $3$'.

Find $P(E | F)$ when two coins are tossed once,where $E$ is the event that no tail appears and $F$ is the event that no head appears.

$A$ coin is tossed three times in succession. If $E$ is the event that there are at least two heads and $F$ is the event in which the first throw is a head,then $P(E|F) = $

In a school,there are $1000$ students,out of which $430$ are girls. It is known that out of $430$,$10\%$ of the girls study in class $XII$. What is the probability that a student chosen randomly studies in class $XII$ given that the chosen student is a girl?

Let $A, B$ and $C$ be three events,which are pairwise independent and $\bar{E}$ denotes the complement of an event $E$. If $P(A \cap B \cap C) = 0$ and $P(C) > 0$,then $P[(\bar{A} \cap \bar{B})|C]$ is equal to