If $A$ and $B$ are any two events such that $P(A) = \frac{2}{5}$ and $P(A \cap B) = \frac{3}{20}$,then the conditional probability $P(A | A' \cup B')$,where $A'$ denotes the complement of $A$,is equal to:

Let $A$ and $B$ be independent events with $P(A)=0.3$ and $P(B)=0.4$. Find $P(B | A)$.

In a class consisting of $40$ boys and $30$ girls,$30 \%$ of the boys and $40 \%$ of the girls are good at Mathematics. If a student selected at random from that class is found to be a girl,then the probability that she is not good at Mathematics is

$A$ coin is tossed until a head appears or it has been tossed thrice. Given that a head does not appear on the first toss,what is the probability that the coin is tossed thrice?

When a die is thrown twice,what is the probability that the sum of the numbers is $6$,given that at least one of the numbers is $4$?

Consider the experiment of throwing a die. If a multiple of $3$ comes up,throw the die again,and if any other number comes,toss a coin. Find the conditional probability of the event 'the coin shows a tail',given that 'at least one die shows a $3$'.