In a manufacturing company,three machines $A$,$B$ and $C$ respectively produce $20 \%$,$30 \%$ and $50 \%$ of the total product. The defective products from $A$,$B$ and $C$ are respectively $5 \%$,$3 \%$ and $2 \%$. If an article produced by the company is selected at random and is found to be defective,then the probability that it is produced by machine $B$ is

Recent studies suggest that $12\%$ of the world population is left-handed. Depending on parents' hand usage, the chances of having left-handed children are as follows: $A$. Both parents are left-handed, chances of having left-handed children = $24\%$. $B$. Both parents are right-handed, chance of having left-handed children = $9\%$. $C$. Father left-handed and mother right-handed, chances of having left-handed children = $17\%$. $D$. Father right-handed and mother left-handed, chances of having left-handed children = $22\%$. Given $P(A) = P(B) = P(C) = P(D) = 1/4$ and $L$ denotes the event that the child is left-handed. What is the probability $P(A|L)$?

There are two balls in an urn. Each ball can be either white or black. If a white ball is put into the urn and thereafter a ball is drawn at random from the urn,then the probability that it is white is

$A$ box contains $n$ coins,$m$ of which are fair and the rest are biased. When a biased coin is tossed,the probability of getting a head is twice as likely as tail. $A$ coin is drawn from the box at random and is tossed twice. It is found that the first time it shows head and the second time it shows tail. Then,the probability that the coin drawn is fair is

Bag $1$ contains $4$ white balls and $5$ black balls,and Bag $2$ contains $n$ white balls and $3$ black balls. One ball is drawn randomly from Bag $1$ and transferred to Bag $2$. $A$ ball is then drawn randomly from Bag $2$. If the probability that the ball drawn from Bag $2$ is white is $29/45$,then $n$ is equal to:

In a certain city, the ratio of men to women is $5:4$. It is found that $80\%$ of men and $90\%$ of women are literate. If a person selected at random is found to be illiterate, then the probability that the person is a man is....