Given two independent events $A$ and $B$ such that $P(A) = 0.3$ and $P(B) = 0.6$. Find $P(A \text{ and not } B)$.

Find $P(E | F)$ when two coins are tossed once,where $E$ is the event that a tail appears on one coin,and $F$ is the event that one coin shows a head.

From a lot containing $n$ good and $m$ bad articles, if $2$ articles are picked at random in succession without replacement, then the probability that the second article picked is bad is

Given that the two numbers appearing on throwing two dice are different,find the probability of the event 'the sum of numbers on the dice is $4$.'

Assume that each born child is equally likely to be a boy or a girl. If a family has two children,what is the conditional probability that both are girls given that at least one is a girl?

$A$ black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than $9,$ given that the black die resulted in a $5$.