There are $3$ bags,each containing $5$ white balls and $3$ black balls. Also,there are $2$ bags,each containing $2$ white balls and $4$ black balls. $A$ white ball is drawn at random. Find the probability that this white ball is from a bag of the first group.

$A$ person is known to speak the truth in $3$ out of $4$ occasions. If he throws a die and reports that it is six,then the probability that it is actually six 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

The contents of $3$ boxes are as follows. If one box is chosen at random and three balls are drawn from it and they are all of different colours,find the probability that they come from Box $2$.
Box $1$ contains $1$ black,$2$ white,$3$ red balls.
Box $2$ contains $1$ black,$1$ white,$2$ red balls.
Box $3$ contains $5$ black,$4$ white,$1$ red balls.

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 $III$?

$A$ 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: