Two cards are drawn one by one at random from a pack of $52$ cards. The probability that both of them are king,is

Two cards are drawn successively with replacement from a pack of $52$ cards. The probability of drawing two aces is

$A$ woman has $10$ keys,out of which only one opens a lock. She tries the keys one after another (keeping aside the failed ones) until she succeeds in opening the lock. What is the probability that the seventh key works?

Consider the circuit. If the probability that each switch is closed is $p$,then find the probability of current flowing through $AB$.

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