$A$ bag consists of $3$ red balls,$5$ blue balls and $8$ green balls. $A$ ball is selected at random. What is the probability of not getting a blue ball?

Two dice are thrown together. The probability that the sum of the numbers is divisible by $2$ or $3$ is

$A$ bag contains $3$ white and $5$ black balls. If one ball is drawn,then the probability that it is black,is

$A$ speaks truth in $20 \%$ of the cases and $B$ in $80 \%$ of the cases. Find the probability that their statements about an incident do not match.

If $A$,$B$,and $C$ are mutually exclusive and exhaustive events of a sample space $S$ such that $P(B) = \frac{3}{2} P(A)$ and $P(C) = \frac{1}{2} P(B)$,then $P(A) = $

When a certain biased die is rolled,a particular face occurs with probability $\frac{1}{6}-x$ and its opposite face occurs with probability $\frac{1}{6}+x$. All other faces occur with probability $\frac{1}{6}$. Note that opposite faces sum to $7$ in any die. If $0 < x < \frac{1}{6}$,and the probability of obtaining a total sum of $7$ when such a die is rolled twice is $\frac{13}{96}$,then the value of $x$ is: