$A$ bag $x$ contains $3$ white balls and $2$ black balls and another bag $y$ contains $2$ white balls and $4$ black balls. $A$ bag and a ball out of it are picked at random. The probability that the ball is white,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:

Three dice are thrown. The sum of the numbers is $15$. What is the chance of getting $4$ on the first die?

$A$ 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:

If a coin is tossed $n$ times,then the probability that the head comes up an odd number of times is:

$A$ bag contains $3$ red,$7$ white,and $4$ black balls. If three balls are drawn from the bag,the probability that all of them are of the same color is: