$25 \%$ of the population are smokers. $A$ smoker has $27$ times more chances to develop lung cancer than a non-smoker. $A$ person is diagnosed with lung cancer and the probability that this person is a smoker is $\frac{k}{10}$. Then the value of $k$ is $.............$

There are $10$ coins in a box, out of which $8$ are normal and the remaining are with heads on both sides. $A$ coin is chosen at random from the box and tossed $6$ times. If it shows heads each time, then the probability that the selected coin has heads on both sides is

Coloured balls are distributed in four boxes as shown in the following table:

Box	Black	White	Red	Blue
$I$	$3$	$4$	$5$	$6$
$II$	$2$	$2$	$2$	$2$
$III$	$1$	$2$	$3$	$1$
$IV$	$4$	$3$	$1$	$5$

$A$ box is selected at random and then a ball is randomly drawn from the selected box. If the colour of the ball is black,what is the probability that the ball drawn is from box $III$?

Bag $I$ contains $3$ red and $2$ green balls and Bag $II$ contains $5$ red and $3$ green balls. $A$ ball is drawn from one of the bags at random and it is found to be green. Then the probability that it is drawn from Bag $I$ is

One card is missing in a pack of $52$ playing cards. If two cards are drawn randomly from the remaining cards at a time and are found to be spades,then the probability that the missing card is not a spade is

Suppose that a bag $A$ contains $n$ red and $2$ black balls and another bag $B$ contains $2$ red and $n$ black balls. One of the two bags is selected at random and two balls are drawn from it at a time. When it is known that the two balls drawn are red,if the probability that those two balls drawn are from bag $A$ is $\frac{6}{7}$,then $n=$