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

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

From a pack of $52$ cards,two cards are drawn one by one without replacement. The probability that the first drawn card is a king and the second is a queen,is

$A$ bag contains $3$ white and $2$ black balls and another bag contains $2$ white and $4$ black balls. $A$ bag is chosen at random and a ball is picked up from it. The probability of the ball being black is:

$A$ bag $X$ contains $2$ white and $3$ black balls and another bag $Y$ contains $4$ white and $2$ black balls. One bag is selected at random and a ball is drawn from it. Then,the probability for the ball chosen to be white is:

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