Cards are drawn one by one without replacement from a pack of $52$ cards. The probability that $10$ cards will precede the first ace is

If $7$ dice are thrown simultaneously,then the probability that all six digits appear on the upper faces is equal to -

Functions are formed from the set $A = \{a_1, a_2, a_3\}$ to another set $B = \{b_1, b_2, b_3, b_4, b_5\}$. If a function is selected at random, the probability that it is a one-one function is

$U_1, U_2, U_3$ are three urns. $U_1$ contains $5$ red,$3$ white,$2$ black balls; $U_2$ contains $4$ red,$4$ white,$2$ black balls and $U_3$ contains $3$ red,$4$ white,$3$ black balls. If a ball is chosen at random from an urn chosen at random,then the probability of not getting a black ball is

Consider the following statements:
Assertion $(A)$: If $P_1, P_2, P_3$ are probabilities of occurrence of three independent events, then the probability of occurrence of at least one of them is $1 - [(1 - P_1)(1 - P_2)(1 - P_3)]$.
Reason $(R)$: For any three independent events $A, B$, and $C$, $P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A)P(B) - P(A)P(C) - P(B)P(C) + P(A)P(B)P(C)$.
The correct option among the following is:

$A$ 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 $r$)