From a pack of $52$ cards,two are drawn with replacement. The probability that the first is a diamond and the second is a king is:

Let $A, B,$ and $C$ be three mutually independent events. Consider the two statements $S_1$ and $S_2$:
$S_1: A$ and $B \cup C$ are independent.
$S_2: A$ and $B \cap C$ are independent.
Then:

If two balanced dice are tossed once,the probability of the event,that the sum of the integers coming on the upper sides of the two dice is $9$,is

$A$ bag contains $6$ white,$7$ red,and $5$ black balls. If $3$ balls are drawn from the bag at random,then the probability that all of them are white is

Three persons work independently on a problem. If the respective probabilities that they will solve it are $\frac{1}{3}$,$\frac{1}{4}$,and $\frac{1}{5}$,then the probability that none can solve it is:

Two cards are drawn from a well-shuffled ordinary deck of $52$ cards. What is the probability that they are both aces if the first card is not replaced?