If a die is rolled twice and the sum of the numbers appearing on them is observed to be $6$,then the probability that the number $1$ appears at least once on them is

If $A$ and $B$ are two events such that $P(A) \neq 0$ and $P(B \mid A) = 1$,then . . . . . . .

Let $A$ and $B$ be two non-null events such that $A \subset B$. Then,which of the following statements is always correct?

An experiment has $10$ equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of $4$ outcomes,the number of outcomes that $B$ must have so that $A$ and $B$ are independent,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
$III.$ $P(A/B) + P(A/B^c) = 1$

Find $P(E | F)$ when two coins are tossed once,where $E$ is the event that no tail appears and $F$ is the event that no head appears.