When a die is thrown twice,what is the probability that the sum of the numbers is $6$,given that at least one of the numbers is $4$?

If $P(A \cap B) = \frac{7}{10}$ and $P(B) = \frac{17}{20}$,where $P$ stands for probability,then $P(A \mid B)$ is equal to:

If the lengths of the sides of a triangle are decided by the three throws of a single fair die,then the probability that the triangle is of maximum area given that it is an isosceles triangle,is

Consider two events $A$ and $B$ such that $P(A) = \frac{1}{4}$,$P(B/A) = \frac{1}{2}$,$P(A/B) = \frac{1}{4}$. For each of the following statements,which is true?
$I.$ $P(A^c/B^c) = \frac{3}{4}$
$II.$ The events $A$ and $B$ are mutually exclusive
$III.$ $P(A/B) + P(A/B^c) = 1$

$A$ number is selected at random from the set $\{1, 2, \ldots, 100\}$. Given that the selected number is divisible by $2$, what is the probability that it is also divisible by $3$ or $5$?

Find $P(E | F)$ for a coin tossed three times,where $E: \text{head on third toss}$,$F: \text{heads on first two tosses}$.