A person is known to speak false once out of 4 times, If that person picks a card at random from a pack of 52 cards and reports that it is a king, then the probability that it is actually a king is

For a binomial variate $X \sim B(n, p)$ the difference between the mean and variance is 1 and the difference between their square is 11 . If the probability of $P(x=2)=m\left(\frac{5}{6}\right)^n$ and $n=36$, then $m: n$

The probability that a man failing to hit a target is $\frac{1}{3}$. If he fires 4 times, then the probability that he hits the target at least thrice is

S is the sample space and $A, B$ are two events of a random experiment. Match the items of List $A$ with the items of List B

$$ \text { List A } $$		$$ \text { List B } $$
I	$A, B$ are mutually exclusive events	a.	$$ P(A \cap B)=P(B)-P(\bar{A}) $$
II	$$ A, B \text { are independent events } $$	b.	$$ P(A) \leq P(B) $$
III	$$ A \cap B=A $$	c.	$$ P\left(\frac{\bar{A}}{B}\right)=1-P(A) $$
IV	$$ A \cup B=S $$	d.	$$ P(A \cup B)=P(A)+P(B) $$
		e.	$$ P(A)+P(B)=2 $$