$A$ couple has two children. Find the probability that both children are males,if it is known that at least one of the children is male.

$A$ candidate takes three tests in succession and the probability of passing the first test is $p$. The probability of passing each succeeding test is $p$ if he passes the preceding one, and $\frac{p}{2}$ if he fails the preceding one. The candidate is selected if he passes at least two tests. The probability that the candidate is selected is:

$A$ box contains $100$ tickets numbered $1, 2, \dots, 100$. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than $10$. What is the probability that the minimum number on them is $5$?

If the events $A$ and $B$ are mutually exclusive,then $P\left( \frac{A}{B} \right) = $

If $A$ and $B$ are two events such that $P(A) = \frac{3}{8}$,$P(B) = \frac{5}{8}$ and $P(A \cup B) = \frac{3}{4}$,then $P(A|B) = $

$A$ bag contains $3$ red and $7$ black balls. Two balls are taken out at random,without replacement. If the first ball taken out is red,what is the probability that the second ball taken out is also red?