The probability that a leap year selected at random contains either $53$ Sundays or $53$ Mondays is

$A$ bag $A$ contains $2$ white and $3$ red balls and bag $B$ contains $4$ white and $5$ red balls. One ball is drawn at random from a randomly chosen bag and is found to be red. The probability that it was drawn from bag $B$ is:

$X$ speaks the truth in $60\%$ of cases and $Y$ in $50\%$ of cases. The probability that they contradict each other while narrating the same incident is

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

If the events $A$ and $B$ are mutually exclusive,then $P\left( \frac{A}{B} \right) = $

$A$ bag contains $6$ white,$7$ red,and $5$ black balls. If $3$ balls are drawn from the bag at random,then the probability that all of them are white is