Find the probability that a two-digit number formed by the digits $1, 2, 3, 4, 5$ is divisible by $4$ (repetition of digits is allowed).

There are two children in a family. The probability that both of them are boys is

If from each of the three boxes containing $3$ white and $1$ black,$2$ white and $2$ black,and $1$ white and $3$ black balls,one ball is drawn at random,then the probability that $2$ white and $1$ black ball will be drawn is

An $URN$ contains $6$ blue,$4$ red,$3$ green and $2$ yellow marbles. If four marbles are picked at random,what is the probability that one is yellow,two are red and one is blue?

Two cards are drawn successively with replacement from a pack of $52$ cards. The probability of drawing two aces 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: