Two cards are drawn from a pack of $52$ cards. What is the probability that both cards are red or both cards are kings?

Two numbers $a$ and $b$ are chosen at random from the set of first $30$ natural numbers. Then the probability that $a^2 - b^2$ is divisible by $3$ is (in $/87$)

Thirty-two persons $X_1, X_2, \ldots, X_{32}$ are randomly seated around a circular table at equal intervals. Two persons $X_i$ and $X_j$ are said to be within earshot of each other if there are at most three persons between them on the minor arc joining $X_i$ and $X_j$. The probability that $X_1$ and $X_3$ are within earshot of each other is:

Three coins are tossed simultaneously. Consider the events $E$: 'three heads or three tails',$F$: 'at least two heads',and $G$: 'at most two heads'. Of the pairs $(E, F)$,$(E, G)$,and $(F, G)$,which are independent and which are dependent?

The probability of getting a sum of $3$,$5$,or $11$ when throwing two dice is:

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: