If four positive integers are selected randomly from the set of positive integers,then the probability that the unit digit of their product is $1, 3, 7,$ or $9$ is:

$A$ bag contains $7$ different black balls and $10$ different red balls. If balls are drawn one by one randomly until all black balls are drawn,what is the probability that this process is completed in the $12^{th}$ draw?

If $A$ and $B$ are two events,then which of the following is $NOT$ true?

$A$ box contains coupons labelled $1, 2, 3, \ldots, n$. $A$ coupon is picked at random and the number $x$ is noted. The coupon is put back into the box and a new coupon is picked at random. The new number is $y$. Then,the probability that one of the numbers $x, y$ divides the other is (in the options below $[r]$ denotes the largest integer less than or equal to $r$)

If $A$ and $B$ are two events,then the probability of the event that at most one of $A$ and $B$ occurs is:

Two numbers are selected randomly from the set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ without replacement one by one. The probability that the minimum of the two numbers is divisible by $3$ or the maximum of the two numbers is divisible by $4$ is: