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:

Suppose $3$ bulbs are selected at random from a lot. Each bulb is tested and classified as defective $(D)$ or non-defective $(N)$. Write the sample space of this experiment.

$A$ die is thrown. Find the probability of the following event: $A$ number more than $6$ will appear.

When two dice are thrown, the probability of getting an ordered pair $(x, y)$ such that $x^2+y^2 \leq 25$, where $x$ and $y$ are the numbers that show up on the two dice, is:

The probability of getting a total of $5$ or $6$ in a single throw of $2$ dice is

Three randomly chosen non-negative integers $x, y$ and $z$ are found to satisfy the equation $x+y+z=10$. Then the probability that $z$ is even,is