$A$ man is known to speak the truth $2$ out of $3$ times. If he throws a die and reports that it is $6$,then the probability that it is actually $5$ 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 $C$?

$A$ pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade is:

An urn contains $5$ balls. Two balls are drawn at random and they are found to be white. The probability that all the balls in the urn are white is:

There are three families $F_1, F_2, F_3$. $F_1$ has $2$ boys and $1$ girl; $F_2$ has $1$ boy and $2$ girls; $F_3$ has $1$ boy and $1$ girl. $A$ family is randomly chosen and a child is chosen from that family randomly. If it is known that the child thus selected is a girl,then the probability that she is from $F_2$ 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: