If $P(A)=0.8, P(B)=0.5$ and $P(B | A)=0.4,$ find $P(A \cap B).$

If $2$ cards drawn at random from a well-shuffled pack of $52$ playing cards are from the same suit,then the probability of getting a face card and a card having a prime number 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 $5$?

$A$ and $B$ are two events such that $P(A) \neq 0$. Find $P(B|A)$,if $A$ is a subset of $B$.

If the lengths of the sides of a triangle are decided by the three throws of a single fair die,then the probability that the triangle is of maximum area given that it is an isosceles triangle,is

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each,then the conditional probability that all children are girls given that at least two are girls is