$4$-digit numbers are formed using the digits $4, 5, 6, 7, 8, 9$ allowing repetition of the given digits. If a number is chosen at random from those numbers thus formed, then the probability that it is exactly divisible by $3$ is

If a number is chosen at random from the set $\{1, 2, 3, \ldots, 100\}$,then the probability that the chosen number is a perfect cube is

$A$ box contains $4$ white pens and $2$ black pens. Another box contains $3$ white pens and $5$ black pens. If one pen is selected from each box,then the probability that both the pens are white is equal to

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
State whether the following statement is true or false and provide a reason:
Statement: $A = B^{\prime}$

$A$ coin and a six-faced die,both unbiased,are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die is:

Two persons $A$ and $B$ throw three unbiased dice one after the other. If $A$ gets a sum of $13$,then the probability that $B$ gets a higher sum is: