$A$ man is known to speak the truth $3$ out of $4$ times. He throws a die and reports that it is a six. The probability that it is actually a six,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?

$A$ man is known to speak the truth $2$ out of $3$ times. If he throws a die and reports that it is $6$,then the probability that it is actually $5$ is:

Bag $I$ contains $3$ red and $2$ green balls and Bag $II$ contains $5$ red and $3$ green balls. $A$ ball is drawn from one of the bags at random and it is found to be green. Then the probability that it is drawn from Bag $I$ is

Bag $A$ contains $2$ white,$1$ black and $3$ red balls and bag $B$ contains $3$ black,$2$ red and $n$ white balls. One bag is chosen at random and $2$ balls drawn from it at random,are found to be $1$ red and $1$ black. If the probability that both balls come from Bag $A$ is $\frac{6}{11}$,then $n$ is equal to

Suppose that a bag $A$ contains $n$ red and $2$ black balls and another bag $B$ contains $2$ red and $n$ black balls. One of the two bags is selected at random and two balls are drawn from it at a time. When it is known that the two balls drawn are red,if the probability that those two balls drawn are from bag $A$ is $\frac{6}{7}$,then $n=$