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

Suppose that $5 \%$ of men and $0.25 \%$ of women have grey hair. $A$ person with grey hair is selected at random. What is the probability of this person being male? Assume that there are equal numbers of males and females.

Bag $A$ contains $4$ green and $3$ red balls and bag $B$ contains $4$ red and $3$ green balls. One bag is selected at random and a ball is drawn,which is found to be green. What is the probability that it was drawn from bag $B$?

$A$ 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

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:

If a machine is correctly set up,it produces $90\%$ acceptable items. If it is incorrectly set up,it produces only $40\%$ acceptable items. Past experience shows that $80\%$ of the set ups are correctly done. If after a certain set up,the machine produces $2$ acceptable items,find the probability that the machine is correctly set up.