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.

$A$ bag contains $(N+1)$ coins: $N$ fair coins,and one coin with 'Head' on both sides. $A$ coin is selected at random and tossed. If the probability of getting 'Head' is $\frac{9}{16}$,then $N$ is equal to:

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

Bag $A$ contains $3$ white and $7$ red balls,and bag $B$ contains $3$ white and $2$ red balls. One bag is selected at random and a ball is drawn from it. What is the probability that the ball was drawn from bag $A$,given that the ball drawn is white?

$A$ 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:

In a bolt factory,machines $A, B$ and $C$ manufacture respectively $20 \%$,$30 \%$ and $50 \%$ of the total bolts. Of their output,$3 \%$,$4 \%$ and $2 \%$ are respectively defective bolts. $A$ bolt is drawn at random from the product. If the bolt drawn is found to be defective,then the probability that it is manufactured by the machine $C$ is