If $A$ and $B$ are two non-mutually exclusive events such that $P(A \mid B) = P(B \mid A)$,then

Find $P(E | F)$ for a coin tossed three times,where $E:$ at most two tails,$F:$ at least one tail. (in $/7$)

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

Bill and George go target shooting together. Both shoot at a target at the same time. Suppose Bill hits the target with probability $0.7$ whereas George,independently,hits the target with probability $0.4$. Given that exactly one shot hit the target,what is the probability that it was George's shot?

Let $E^c$ denote the complement of an event $E$. Let $E, F, G$ be pairwise independent events with $P(G)>0$ and $P(E \cap F \cap G) = 0$. Then $P(E^c \cap F^c \mid G)$ equals

$P(A / A \cap B) + P(B / A \cap B) =$