$A$ bag contains $5$ white,$7$ black and $4$ red balls. Three balls are drawn from the bag at random,then the probability that all the three balls are white,is

There are $3$ bags which are known to contain $2$ white and $3$ black balls; $4$ white and $1$ black balls and $3$ white and $7$ black balls respectively. $A$ ball is drawn at random from one of the bags and found to be a black ball. Then the probability that it was drawn from the bag containing the most black balls is

The probability that a leap year selected randomly will have $53$ Sundays is

$A$ cricket team has $15$ members,of whom only $5$ can bowl. If the names of the $15$ members are put into a hat and $11$ are drawn at random,then the probability of obtaining a team of $11$ containing at least $3$ bowlers is

Two numbers $a$ and $b$ are chosen at random from the set of first $30$ natural numbers. The probability that $a^2 - b^2$ is divisible by $3$ is

An ordinary cube has four blank faces,one face marked $2$,and another marked $3$. The probability of obtaining a total of exactly $12$ in $5$ throws is: