$A$ five-digit number is formed by writing the digits $1, 2, 3, 4, 5$ in a random order without repetition. What is the probability that the number is divisible by $4$?

$A$ bag contains $13$ red,$14$ green,and $15$ black balls. The probability of getting exactly $2$ black balls when pulling out $4$ balls is ${P_1}$. Now,the number of balls of each color is doubled,and $8$ balls are pulled out. The probability of getting exactly $4$ black balls is ${P_2}$. Then:

What is the probability of getting a total of less than $12$ in the throw of two dice?

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

Three mangoes and three apples are in a box. If two fruits are chosen at random,the probability that one is a mango and the other is an apple is

$A$ bag contains $3$ black and $4$ white balls. Two balls are drawn one by one at random without replacement. The probability that the second drawn ball is white,is