Three cards are drawn successively,without replacement from a pack of $52$ well-shuffled cards. What is the probability that the first two cards are kings and the third card drawn is an ace?

$A$ and $B$ are two independent events such that $P(A) = \frac{1}{2}$ and $P(B) = \frac{1}{3}$. Then $P$ (neither $A$ nor $B$) is equal to

If $P(A_1 \cup A_2) = 1 - P(A_1^c) P(A_2^c)$,where $c$ stands for complement,then the events $A_1$ and $A_2$ are

There are $3$ bags $A, B$ and $C$. Bag $A$ contains $2$ white and $3$ black balls,bag $B$ contains $4$ white and $2$ black balls and Bag $C$ contains $3$ white and $2$ black balls. If a ball is drawn at random from a randomly chosen bag,then the probability that the ball drawn is black,is

An urn contains $4$ red and $5$ white balls. Two balls are drawn one after the other without replacement,then the probability that both the balls are red is

Two marbles are drawn in succession from a box containing $10$ red,$30$ white,$20$ blue and $15$ orange marbles,with replacement being made after each drawing. Then the probability,that the first drawn marble is red and the second drawn marble is white,is