Let $A, B, C$ be pairwise independent events such that $P(C) > 0$ and $P(A \cap B \cap C) = 0$. Then $P(A' \cap B'|C)$ is equal to:

For a biased die,the probabilities for different faces to turn up are

$Face$	$1$	$2$	$3$	$4$	$5$	$6$
$P(F)$	$0.2$	$0.22$	$0.11$	$0.25$	$0.05$	$0.17$

The die is tossed and you are told that either face $4$ or face $5$ has turned up. The probability that it is face $4$ is

Evaluate $P(A \cup B)$,if $2 P(A) = P(B) = \frac{5}{13}$ and $P(A|B) = \frac{2}{5}$.

$A$ and $B$ are two events such that $P(A) \neq 0$. Find $P(B|A)$,if $A$ is a subset of $B$.

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

Let $A$ and $E$ be any two events with positive probabilities:
Statement $- 1$: $P(E/A) \geq P(A/E)P(E)$
Statement $- 2$: $P(A/E) \geq P(A \cap E)$