$A$ 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:

In a certain recruitment test with multiple choice questions,there are four options to answer each question,out of which only one is correct. An intelligent student knows $90 \%$ of the correct answers,while a weak student knows only $20 \%$ of the correct answers. If an intelligent student gets the correct answer for a question,what is the probability that he was guessing it?

$A$ box $A$ contains $2$ white,$3$ red and $2$ black balls. Another box $B$ contains $4$ white,$2$ red and $3$ black balls. If two balls are drawn at random,without replacement,from a randomly selected box and one ball turns out to be white while the other ball turns out to be red,then the probability that both balls are drawn from box $B$ is

In a college,$25\%$ of the boys and $10\%$ of the girls offer Mathematics. The girls constitute $60\%$ of the total number of students. If a student is selected at random and is found to be studying Mathematics,the probability that the student is a girl,is

There are three coins. One is a two-headed coin (having heads on both faces),another is a biased coin that comes up heads $75 \%$ of the time,and the third is an unbiased coin. One of the three coins is chosen at random and tossed; it shows heads. What is the probability that it was the two-headed coin?

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.