Two dice $A$ and $B$ are rolled. If it is known that the number on $B$ is $5$, then the probability that the sum of the numbers on the two dice will be greater than $9$ is

Suppose $E$ and $F$ are two events of a random experiment. If the probability of occurrence of $E$ is $1/5$ and the probability of occurrence of $F$ given $E$ is $1/10$, then the probability of non-occurrence of at least one of the events $E$ and $F$ is

$A$ and $B$ are mutually exclusive events of a random experiment and $P(B) \neq 1$,then $P(A \mid B^c) =$

An urn contains $5$ red and $5$ black balls. $A$ ball is drawn at random,its colour is noted and is returned to the urn. Moreover,$2$ additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?

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

$A$ bag contains $N$ balls out of which $3$ are white,$6$ are green,and the remaining $(N-9)$ balls are blue. Three balls are drawn randomly one after the other without replacement. Let $W_i, G_i$,and $B_i$ denote the events that the ball drawn in the $i^{\text{th}}$ draw is white,green,and blue,respectively. If $P(W_1 \cap G_2 \cap B_3) = \frac{2}{5N}$ and $P(B_3 \mid W_1 \cap G_2) = \frac{2}{9}$,then $N$ equals: