If $A$ and $B$ are any two events such that $P(A)+P(B)-P(A \cap B)=P(A)$,then

If $A$ and $B$ are any two events of a random experiment and $P(B) \neq 1$,then $P(A | B^c) =$ ?

An urn $A$ contains $3$ white and $5$ black balls. Another urn $B$ contains $6$ white and $8$ black balls. $A$ ball is picked from $A$ at random and then transferred to $B$. Then,a ball is picked at random from $B$. The probability that it is a white ball is

Consider three sets $E_1=\{1,2,3\}, F_1=\{1,3,4\}$ and $G_1=\{2,3,4,5\}$. Two elements are chosen at random,without replacement,from the set $E_1$,and let $S_1$ denote the set of these chosen elements.
Let $E_2=E_1-S_1$ and $F_2=F_1 \cup S_1$. Now two elements are chosen at random,without replacement,from the set $F_2$ and let $S_2$ denote the set of these chosen elements.
Let $G_2=G_1 \cup S_2$. Finally,two elements are chosen at random,without replacement,from the set $G_2$ and let $S_3$ denote the set of these chosen elements.
Let $E_3=E_2 \cup S_3$. Given that $E_1=E_3$,let $p$ be the conditional probability of the event $S_1=\{1,2\}$. Then the value of $p$ is

Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is $11$,given that $5$ appears on the first die?

If $2$ cards drawn at random from a well-shuffled pack of $52$ playing cards are from the same suit,then the probability of getting a face card and a card having a prime number is