$A$ man is known to speak the truth $3$ out of $4$ times. He throws a die and reports that it is a six. The probability that it is actually a six,is

$A$ bag contains $6$ balls. If three balls are drawn at a time and all of them are found to be green,then the probability that exactly $5$ of the balls in the bag are green is:

$A$ boy speaks the truth in $3$ out of $5$ times. If he throws a die and reports that the number appeared on it is $5$,then the probability that it is actually $5$ is:

$A$ computer producing factory has only two plants $T_1$ and $T_2$. Plant $T_1$ produces $20 \%$ and plant $T_2$ produces $80 \%$ of the total computers produced. $7 \%$ of computers produced in the factory turn out to be defective. It is known that $P(\text{defective} | T_1) = 10 P(\text{defective} | T_2)$. $A$ computer produced in the factory is randomly selected and it is not defective. Then the probability that it is produced in plant $T_2$ is

$25 \%$ 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 $.............$

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 $III$?