If three numbers are randomly selected from the set $\{1, 2, 3, \ldots, 50\}$, then the probability that they are in arithmetic progression is

$2$ aeroplanes $I$ and $II$ bomb a target in succession. The probabilities of $I$ and $II$ scoring a hit correctly are $0.3$ and $0.2$ respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the $2^{nd}$ plane is

The probability of occurrence of an event is $\frac{2}{5}$ and the probability of non-occurrence of another event is $\frac{3}{10}$. If these events are independent,then the probability that only one of the two events occur is

If the probabilities of three independent events occurring are $p_1, p_2, p_3$,what is the probability that at least one of these events occurs?

Let $0 < P(A) < 1$,$0 < P(B) < 1$ and $P(A \cup B) = P(A) + P(B) - P(A)P(B).$ Then

$A$ 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 $r$)