The probability that a number selected at random from the set of numbers $(1, 2, 3, \ldots, 100)$ is a cube,is

$A$ fair coin and an unbiased die are tossed. Let $A$ be the event 'head appears on the coin' and $B$ be the event '$3$ on the die'. Check whether $A$ and $B$ are independent events or not.

Two dice are rolled one after the other. The probability that the number on the first die is smaller than the number on the second die is

When two dice are thrown, the probability of getting a prime number on one die and a composite number on the other is

An integer is chosen from the set $\{2k \mid -9 \leq k \leq 10\}$. The probability that the chosen integer is divisible by both $4$ and $6$ is

In the random experiment of tossing two unbiased dice, let $E$ be the event of getting the sum $8$ and $F$ be the event of getting even numbers on both the dice. Then:
$I. P(E) = \frac{7}{36}$
$II. P(F) = \frac{1}{3}$
Which of the following is a correct statement?