$A$ card from a pack of $52$ cards is lost. From the remaining cards of the pack,two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.

$70 \%$ of the total employees of a factory are men. Among the employees of that factory,$30 \%$ of men and $15 \%$ of women are technical assistants. If an employee chosen at random is found to be a technical assistant,then the probability that this employee is a man is

$A$ factory has a total of three manufacturing units,$M_1, M_2$,and $M_3$,which produce bulbs independently. The units $M_1, M_2$,and $M_3$ produce bulbs in the proportions of $2: 2: 1$,respectively. It is known that $20\%$ of the bulbs produced in the factory are defective. It is also known that,of all the bulbs produced by $M_1, 15\%$ are defective. Suppose that,if a randomly chosen bulb produced in the factory is found to be defective,the probability that it was produced by $M_2$ is $\frac{2}{5}$. If a bulb is chosen randomly from the bulbs produced by $M_3$,then the probability that it is defective is $.....$ .

Three similar urns $A, B, C$ contain $2$ red and $3$ white balls; $3$ red and $2$ white balls; $1$ red and $4$ white balls respectively. If a ball selected at random from one of the urns is found to be red,then the probability that it is drawn from urn $C$ is

Suppose we have four boxes $A, B, C$ and $D$ containing coloured marbles as given below:

Box	Red	White	Black
$A$	$1$	$6$	$3$
$B$	$6$	$2$	$2$
$C$	$8$	$1$	$1$
$D$	$0$	$6$	$4$

One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red,what is the probability that it was drawn from box $A$,box $B$,or box $C$?

$A$ letter is known to have arrived by post either from $KANPUR$ or from $ANANTPUR$. On the envelope,just two consecutive letters $AN$ are visible. The probability that the letter came from $ANANTPUR$ is: