$A$ bag contains $3$ white and $2$ red balls. If the first ball drawn is not replaced,what is the probability that the second ball is red?

Find $P(E | F)$ for a coin tossed three times,where $E:$ at most two tails,$F:$ at least one tail. (in $/7$)

If $A$ and $B$ are two events such that $P(A) \neq 0$ and $P(B | A)=1$,then:

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:

If $A$ and $B$ are two independent events,then $P\left( \frac{A}{B} \right) = $

If $A$ and $B$ are two events such that $P(A | B) = 0.6$,$P(B | A) = 0.3$,and $P(A) = 0.1$,then $P(\bar{A} \cap \bar{B})$ equals: