If the events $A$ and $B$ are mutually exclusive,then $P\left( \frac{A}{B} \right) = $

An electronic assembly consists of two subsystems,$A$ and $B$. From previous testing procedures,the following probabilities are known:
$P(A \text{ fails}) = 0.2$
$P(B \text{ fails alone}) = 0.15$
$P(A \text{ and } B \text{ fail}) = 0.15$
Evaluate the probability $P(A \text{ fails } | \text{ } B \text{ has failed})$.

$A$ coin is tossed until a head appears or it has been tossed thrice. Given that a head does not appear on the first toss,what is the probability that the coin is tossed thrice?

$A$ box contains $3$ white and $2$ red balls. $A$ ball is drawn and another ball is drawn without replacing the first ball. What is the probability that the second ball is red?

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

$A$ black and a red dice are rolled. Find the conditional probability of obtaining the sum $8$,given that the red die resulted in a number less than $4$.