$A$ draws two cards with replacement from a pack of $52$ cards and $B$ throws a pair of dice. What is the chance that $A$ gets both cards of the same suit and $B$ gets a total of $6$?

$A$ and $B$ are independent events. The probability that both $A$ and $B$ occur is $\frac{1}{20}$ and the probability that neither of them occurs is $\frac{3}{5}$. The probability of occurrence of $A$ is

The probability that a randomly chosen $2 \times 2$ matrix with all the entries from the set of first $10$ primes is singular,is equal to

Let $S = \{1, 2, \dots, 20\}$. $A$ subset $B$ of $S$ is said to be "nice" if the sum of the elements of $B$ is $203$. Then the probability that a randomly chosen subset of $S$ is "nice" is

$A$ bag contains $2$ white,$3$ green,and $5$ red balls. If three balls are drawn one after the other without replacement,then the probability that the last ball drawn was red is

Football teams $T_1$ and $T_2$ play two games against each other. The outcomes of the two games are independent. The probabilities of $T_1$ winning,drawing,and losing a game against $T_2$ are $\frac{1}{2}$,$\frac{1}{6}$,and $\frac{1}{3}$,respectively. Each team gets $3$ points for a win,$1$ point for a draw,and $0$ points for a loss. Let $X$ and $Y$ denote the total points scored by teams $T_1$ and $T_2$,respectively,after two games.
$(1)$ $P(X>Y)$ is
$(A)$ $\frac{1}{4}$ $(B)$ $\frac{5}{12}$ $(C)$ $\frac{1}{2}$ $(D)$ $\frac{7}{12}$
$(2)$ $P(X=Y)$ is
$(A)$ $\frac{11}{36}$ $(B)$ $\frac{1}{3}$ $(C)$ $\frac{13}{36}$ $(D)$ $\frac{1}{2}$