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 $/7$)?

In a school,there are $1000$ students,out of which $430$ are girls. It is known that out of $430$,$10\%$ of the girls study in class $XII$. What is the probability that a student chosen randomly studies in class $XII$ given that the chosen student is a girl?

If $P(A) = \frac{1}{2}$,$P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$,then $P(B/A) = $

If $A$ and $B$ are two events such that $P(A) \neq 0$ and $P(B) \neq 1$,then $P\left( \frac{\overline{A}}{\overline{B}} \right) = $

If $A$ and $B$ are two events such that $P(A) = \frac{2}{3}$, $P(B) = \frac{1}{2}$ and $P(A | B) = \frac{2}{3}$, then $P(A' \cup B) + P(A \cup B') = $

Let $S$ be the sample space of all $3 \times 3$ matrices with entries from the set $\{0, 1\}$. Let the events $E_1$ and $E_2$ be given by $E_1 = \{A \in S : \operatorname{det} A = 0\}$ and $E_2 = \{A \in S : \text{sum of entries of } A \text{ is } 7\}$. If a matrix is chosen at random from $S$,then the conditional probability $P(E_1 \mid E_2)$ equals: