In a toy factory,machines $A, B$,and $C$ are used to manufacture $30 \%, 40 \%$,and $30 \%$ of the output,respectively. The probabilities of toys made by machines $A, B$,and $C$ being defective are $2 \%, 3 \%$,and $1 \%$,respectively. $A$ toy is taken from the factory and is found to be defective. The probability that it was manufactured by machine $B$ is

In a school there are $3$ sections $A, B$ and $C$. Section $A$ contains $20$ girls and $30$ boys,section $B$ contains $40$ girls and $20$ boys and section $C$ contains $10$ girls and $30$ boys. The probabilities of selecting the section $A, B$ and $C$ are $0.2, 0.3$ and $0.5$ respectively. If a student selected at random from the school is a girl,then the probability that she belongs to section $A$ is

$A$ bag $P$ contains $5$ white marbles and $3$ black marbles. Four marbles are drawn at random from $P$ and are put in an empty bag $Q$. If a marble drawn at random from $Q$ is found to be black,then the probability that all the three black marbles in $P$ were transferred to the bag $Q$ is:

There are three bags $X$,$Y$,and $Z$. Bag $X$ contains $5$ one-rupee coins and $4$ five-rupee coins; Bag $Y$ contains $4$ one-rupee coins and $5$ five-rupee coins; and Bag $Z$ contains $3$ one-rupee coins and $6$ five-rupee coins. $A$ bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability that it came from bag $Y$ is:

Of the students in a college,it is known that $60 \%$ reside in a hostel and $40 \%$ are day scholars (not residing in a hostel). Previous year results report that $30 \%$ of all students who reside in a hostel attain $A$ grade and $20 \%$ of day scholars attain $A$ grade in their annual examination. At the end of the year,one student is chosen at random from the college and they have an $A$ grade. What is the probability that the student is a hostler?

The following table shows the probability of selecting the boxes $A, B$ and $C$ and the number of balls of different colours contained in them. If a ball is selected at random and it is found to be green,what is the probability that it was selected from box $C$?

Box	White	Green	Red	Probability
$A$	$1$	$2$	$3$	$\frac{1}{2}$
$B$	$2$	$3$	$1$	$\frac{1}{3}$
$C$	$3$	$1$	$2$	$\frac{1}{6}$