$A$ biased die is tossed and the respective probabilities for various faces to turn up are given below:

$Face$	$1$	$2$	$3$	$4$	$5$	$6$
$P(F)$	$0.1$	$0.24$	$0.19$	$0.18$	$0.15$	$0.14$

If an even face has turned up,then the probability that it is face $2$ or face $4$ is:

$A$ die is thrown twice and the sum of the numbers appearing is observed to be $6$. What is the conditional probability that the number $4$ has appeared at least once?

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:

Two events $E$ and $F$ are independent. If $P(E) = \frac{3}{5}$ and $P(F) = \frac{3}{10}$, then $P(E'/F) + P(F'/E) = \text{ . . . . . . }$

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

If $E_{1}$ denotes the event of getting a sum of $6$ when throwing two dice and $E_{2}$ is the event of getting a $2$ on at least one of the two dice,then $P(E_{2} / E_{1})$ is (in $/ 5$)