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.

$A$ 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:

Two bags $A$ and $B$ contain $2$ white,$3$ black,$4$ red balls and $3$ white,$4$ black,$5$ red balls respectively. $A$ ball is drawn from bag $A$ and transferred to bag $B$. If a ball is then drawn from bag $B$,what is the probability that the ball drawn from bag $B$ is white?

$A$ 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

$A$ manufacturer has three machine operators $A$,$B$,and $C$. The first operator $A$ produces $1 \%$ defective items,whereas the other two operators $B$ and $C$ produce $5 \%$ and $7 \%$ defective items respectively. $A$ is on the job for $50 \%$ of the time,$B$ is on the job for $30 \%$ of the time,and $C$ is on the job for $20 \%$ of the time. If a defective item is produced,what is the probability that it was produced by $A$ (in $/34$)?

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