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

Ten cards numbered $1$ to $10$ are placed in a box,mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than $3,$ what is the probability that it is an even number (in $/7$)?

Let $E^c$ denote the complement of an event $E$. Let $E, F, G$ be pairwise independent events with $P(G)>0$ and $P(E \cap F \cap G) = 0$. Then $P(E^c \cap F^c \mid G)$ equals

If $A$ and $B$ are two events such that $P(\bar{A})=0.3, P(B)=0.4$ and $P(A \cap \bar{B})=0.5$, then $P(B \mid A \cup \bar{B})=$

$A$ and $B$ are independent events of a random experiment if and only if

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