If $E_{1}$ denotes the event of getting a sum of $6$ when throwing two dice and $E_{2}$ is the event of getting a $2$ on at least one of the two dice,then $P(E_{2} / E_{1})$ is (in $/ 5$)

$A$ coin is tossed three times. If event $E$ represents getting at least two heads and event $F$ represents getting a head on the first toss,find $P(E|F)$.

Let $A$ and $B$ be two events with $P(A^{C}) = 0.3$,$P(B) = 0.4$,and $P(A \cap B^{C}) = 0.5$. Then $P(B \mid A \cup B^{C})$ is equal to

When $2$ dice are thrown,it is observed that the sum of the numbers appearing on the top faces of both dice is a prime number. What is the probability that at least one of the numbers in the pair is a multiple of $3$?

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 $P(A \text{ fails } | \text{ } B \text{ has failed})$.

If $A$ and $B$ are two events such that $P(\bar{A})=0.3, P(B)=0.4$ and $P(A \cap \bar{B})=0.5$,then $P(B \mid A \cup \bar{B})=$