There are three families $F_1, F_2, F_3$. $F_1$ has $2$ boys and $1$ girl; $F_2$ has $1$ boy and $2$ girls; $F_3$ has $1$ boy and $1$ girl. $A$ family is randomly chosen and a child is chosen from that family randomly. If it is known that the child thus selected is a girl,then the probability that she is from $F_2$ 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?

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

Bag $I$ contains $3$ red and $4$ black balls,while Bag $II$ contains $5$ red and $6$ black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag $II$.

An urn contains $7$ red, $5$ white and $3$ black balls. Three balls are drawn randomly one after the other without replacement. If it is known that the first ball drawn is red and the second ball drawn is white, then the probability that the third ball drawn is not red is

$A$ dealer gets refrigerators from $3$ different manufacturing companies $C_1, C_2$ and $C_3$. $25 \%$ of his stock is from $C_1, 35 \%$ from $C_2$ and $40 \%$ from $C_3$. The percentages of receiving defective refrigerators from $C_1, C_2$ and $C_3$ are $3 \%, 2 \%$ and $1 \%$ respectively. If a refrigerator sold at random is found to be defective by a customer, then the probability that it is from $C_2$ is