If events $A$ and $B$ are such that $P(A) = \frac{1}{4}$, $P(A \cap B) = \frac{1}{10}$ and $P(A|B) = 2P(B|A)$, then $P(B) = ..........$

Let $E^{C}$ denote the complement of an event $E$. Let $E_{1}, E_{2}$ and $E_{3}$ be any pairwise independent events with $P(E_{1}) > 0$ and $P(E_{1} \cap E_{2} \cap E_{3}) = 0$. Then $P(E_{2}^{C} \cap E_{3}^{C} / E_{1})$ 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 $3$?

$A$ 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?

Let $A, B$ and $C$ be three events,which are pairwise independent and $\overline{E}$ denote the complement of an event $E$. If $P(A \cap B \cap C) = 0$ and $P(C) > 0$,then $P((\overline{A} \cap \overline{B}) / C)$ is equal to

Two cards are drawn one by one from a pack of cards. The probability of getting the first card as an ace and the second as a coloured card is (without replacement).