$A$ bag contains $3$ white and $2$ red balls. If the first ball drawn is not replaced,what is the probability that the second ball is red?

Compute $P(A | B),$ if $P(B)=0.5$ and $P(A \cap B)=0.32$.

Find $P(E | F)$ for a die thrown three times,where $E: 4$ appears on the third toss,and $F: 6$ and $5$ appear respectively on the first two tosses.

$A$ bag contains $4$ Red and $6$ Black balls. $A$ ball is drawn at random from the bag,its colour is observed and this ball along with $3$ additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag,then the probability that this drawn ball is red is

Let $A$ and $B$ be two events with $P(A) = \frac{1}{7}$,$P(A|B) = \frac{2}{3}$,and $P(B) = \frac{2}{7}$. Then,the value of $P(B|A)$ is

If $P(A) = \frac{6}{11}$,$P(B) = \frac{5}{11}$ and $P(A \cup B) = \frac{7}{11}$,then $P(A \mid B) = $ . . . . . . .