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

Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that one of them is black and the other is red.

If a man throws a die until he gets a number bigger than $3$,then the probability that he gets a $5$ in his last throw is

$A$ bag contains $n + 1$ coins. Among these coins,one coin has heads on both sides,while all other coins are fair. $A$ coin is chosen at random from the bag. If the probability of getting a head when the chosen coin is tossed is $7/12$,what is the value of $n$?

If $A$ and $B$ are two independent events such that $P(A) = \frac{1}{2}$ and $P(B) = \frac{1}{5}$,then which of the following is true?

If $A$ and $B$ are independent events of a random experiment such that $P(A \cap B) = \frac{1}{6}$ and $P(\bar{A} \cap \bar{B}) = \frac{1}{3}$,then $P(A)$ is equal to (Here,$\bar{E}$ is the complement of the event $E$)