What is the probability that a randomly selected leap year has $53$ Sundays or $53$ Mondays (in $/7$)?

$A$ fair coin with $1$ marked on one face and $6$ on the other and a fair die are both tossed. Find the probability that the sum of the numbers that turn up is $12$.

$A$ fair die is thrown at random. Let $A$ be the event that the number obtained on the die is a non-even prime number and $B$ be the event that the number obtained on the die is an odd number. Let $p : P(A) = \frac{1}{3}$; $q : A$ and $B$ are independent events. Then the truth values of statements $p$ and $q$ respectively are.....

Let $A$ and $B$ be two events such that $P(\overline{A \cup B}) = \frac{1}{6}$,$P(A \cap B) = \frac{1}{4}$ and $P(\bar{A}) = \frac{1}{4}$,where $\bar{A}$ stands for the complement of the event $A$. Then the events $A$ and $B$ are

Let $A$ and $B$ be two events such that $P(A \cap B) = \frac{1}{6}$, $P(A \cup B) = \frac{31}{45}$, and $P(\bar{B}) = \frac{7}{10}$, then:

If $\frac{1 + 3p}{3}, \frac{1 - p}{4}$ and $\frac{1 - 2p}{2}$ are the probabilities of three mutually exclusive events,then the set of all values of $p$ is