In a single throw of $2$ dice,find the probability of getting a total of $8.$

The probability of an impossible event,i.e.,$P(\phi)$,is:

$A$ box contains $6$ black and $4$ red balls. Three balls are drawn at random. What is the probability that one ball is red and the other two are black?

$A$ bag contains $3$ red,$4$ white and $5$ blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour is

$A$ bag contains $30$ balls numbered from $1$ to $30$. One ball is drawn randomly. The probability that the number on the ball is a multiple of $5$ or $7$ 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