$A, B, C$ are mutually exclusive events such that $P(A) = \frac{3x+1}{3}$,$P(B) = \frac{1-x}{4}$,and $P(C) = \frac{1-2x}{2}$. Then the set of possible values of $x$ is:

$A$ and $B$ are two independent events such that $P(A \cup B) = 0.8$ and $P(A) = 0.3$. The value of $P(B)$ is:

$A$ random variable $X$ has the following probability distribution:
| $X=x$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| $P(X=x)$ | $0.15$ | $0.23$ | $0.12$ | $0.20$ | $0.08$ | $0.10$ | $0.05$ | $0.07$ |
For the events $E = \{X \text{ is a prime number}\}$ and $F = \{X < 5\}$,find $P(E \cup F)$.

Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that one of them is black and the other is red.

$A$ and $B$ alternately throw a pair of dice. $A$ wins if he throws a sum of $5$ before $B$ throws a sum of $8$,and $B$ wins if he throws a sum of $8$ before $A$ throws a sum of $5$. The probability that $A$ wins,if $A$ makes the first throw,is

If a man throws a die until he gets a number bigger than $3$,then the probability that he gets a $5$ in his last throw is