If $A$ and $B$ are two events such that $P(A \cup B) = P(A \cap B)$,then the true relation is

$A$ coin is tossed until a head appears or it has been tossed thrice. Given that a head does not appear on the first toss,what is the probability that the coin is tossed thrice?

$A$ bag contains $ 17 $ tickets numbered from $ 1 $ to $ 17 $. $A$ ticket is drawn at random,then another ticket is drawn without replacing the first one. The probability that both the tickets show even numbers is

$A$ candidate takes three tests in succession and the probability of passing the first test is $p$. The probability of passing each succeeding test is $p$ if he passes the preceding one,and $\frac{p}{2}$ if he fails the preceding one. The candidate is selected if he passes at least two tests. The probability that the candidate is selected is:

Consider the experiment of tossing a coin. If the coin shows head,toss it again but if it shows tail,then throw a die. Find the conditional probability of the event that 'the die shows a number greater than $4$' given that 'there is at least one tail'.

Two integers $r$ and $s$ are drawn one at a time without replacement from the set $\{1, 2, \ldots, n\}$. Then $P(r \leq k \mid s \leq k) =$