If two events $A$ and $B$ are such that $P(A \cup B) = \frac{5}{6}$,$P(A \cap B) = \frac{1}{3}$,and $P(\bar{A}) = \frac{1}{2}$,then the events $A$ and $B$ are:

One card is drawn at random from a well-shuffled pack of $52$ cards. The probability that the card drawn is a face card (Jack,Queen,and King only) is

Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment:
$A:$ the sum is even.
$B:$ the sum is a multiple of $3$.
$C:$ the sum is less than $4$.
$D:$ the sum is greater than $11$.
Which pairs of these events are mutually exclusive?

The probabilities of $A$ and $B$ dying in a year are $p$ and $q$ respectively. What is the probability that only one of them will be alive at the end of the year?

When two dice are thrown,the probability of getting the sum of the values on them as $10$ or $11$ is

If any four numbers are selected,what is the probability that the last digit of their product will be $1, 3, 5$ or $7$?