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:

An unbiased die is thrown twice. Let the event $A$ be 'odd number on the first throw' and $B$ the event 'odd number on the second throw'. Check the independence of the events $A$ and $B$.

From a group of $8$ boys and $3$ girls,a committee of $5$ members is to be formed. Find the probability that $2$ particular girls are included in the committee.

If $E_{1}$ denotes the event of getting a sum of $6$ when throwing two dice and $E_{2}$ is the event of getting a $2$ on at least one of the two dice,then $P(E_{2} / E_{1})$ is (in $/ 5$)

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
$III.$ $P(A/B) + P(A/B^c) = 1$

Find $P(E | F)$ when two coins are tossed once,where $E$ is the event that a tail appears on one coin,and $F$ is the event that one coin shows a head.