There are $2$ bags each containing $3$ white and $5$ black balls and $4$ bags each containing $6$ white and $4$ black balls. If a ball drawn randomly from a bag is found to be black,then the probability that this ball is from the first set of bags is

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 one of the two bags and it is found to be red. Find the probability that the ball was drawn from bag $B$.

From a certain population, the probability of choosing a colour blind man is $\frac{1}{20}$ and that of a colour blind woman is $\frac{1}{10}$. If a randomly chosen person is found to be colour blind, then the probability that the person is a man is

Two coins $A$ and $B$ are kept in an urn. When coin $A$ is flipped,the probability of getting a head is $1/4$,while for coin $B$ it is $3/4$. One coin is randomly chosen from this bag,tossed twice,and it falls heads on both occasions. The probability that it is coin $A$ is:

Given three identical boxes $I$,$II$ and $III$,each containing two coins. In box $I$,both coins are gold coins,in box $II$,both are silver coins and in the box $III$,there is one gold and one silver coin. $A$ person chooses a box at random and takes out a coin. If the coin is of gold,what is the probability that the other coin in the box is also of gold?

There are two dice $A$ and $B$. Die $A$ has $4$ red and $2$ white faces,and die $B$ has $2$ red and $4$ white faces. $A$ coin is tossed once. If it shows head,die $A$ is rolled; if it shows tail,die $B$ is rolled. If the probability that die $A$ is used is $\left(\frac{32}{33}\right)$ given that red turns up every time in the first $n$ throws,then $n=$