Let $A$ and $B$ be events for which $P(A) = x$,$P(B) = y$,and $P(A \cap B) = z$. Then $P(\bar{A} \cap B)$ equals:

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the events $B$ and $C$.

An unbiased dice with faces marked $1, 2, 3, 4, 5,$ and $6$ is rolled four times. Out of the four face values obtained,the probability that the minimum face value is not less than $2$ and the maximum face value is not greater than $5$ is: (in $/ 81$)

The probability that a leap year selected randomly will have $53$ Sundays is

Check whether the following probabilities $P(A) = 0.5$,$P(B) = 0.4$,and $P(A \cup B) = 0.8$ are consistently defined.

$A$ rational number is selected at random from the distinct rational numbers of the form $p/q$ formed with $p$ and $q$ belonging to the set $\{1, 2, 3, 4, 5, 6\}$. The probability that the rational number selected is a proper fraction is: