Meera visits only one of the two temples $A$ and $B$ in her locality. The probability that she visits temple $A$ is $\frac{2}{5}$. If she visits temple $A$,the probability that she meets her friend is $\frac{1}{3}$,whereas it is $\frac{2}{7}$ if she visits temple $B$. Meera met her friend at one of the two temples. The probability that she met her at temple $B$ is

In a factory which manufactures bolts,machines $A, B$ and $C$ manufacture respectively $25\%, 35\%$ and $40\%$ of the bolts. Of their outputs,$5, 4$ and $2$ percent are respectively defective bolts. $A$ bolt is drawn at random from the product and is found to be defective. What is the probability that it is manufactured by the machine $B$?

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

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?

Suppose a girl throws a die. If she gets a $5$ or $6,$ she tosses a coin three times and notes the number of heads. If she gets $1, 2, 3$ or $4,$ she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head,what is the probability that she threw $1, 2, 3$ or $4$ with the die?

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
$A$	$1$	$2$	$3$	$\frac{1}{2}$
$B$	$2$	$3$	$1$	$\frac{1}{3}$
$C$	$3$	$1$	$2$	$\frac{1}{6}$