If $A$ and $B$ are two events of a random experiment,$P(A) = 0.25$,$P(B) = 0.5$ and $P(A \cap B) = 0.15$,then $P(A \cap \bar{B}) = $

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:

Three coins are tossed. Describe two events which are mutually exclusive but not exhaustive.

The probabilities of two persons to hit a target are $\frac{1}{4}$ and $\frac{1}{5}$ respectively. The probability that the target is being hit when both of them attempt independently is

What is the probability of getting a doublet when two dice are thrown?

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