From the word $POSSESSIVE$,a letter is chosen at random. The probability of it being $S$ is

The probability of obtaining an even prime number on each die,when a pair of dice is rolled,is . . . . . . .

For two events $A$ and $B$,if $P(A \cup B) = \frac{3}{4}$,$P(A \cap B) = \frac{1}{4}$,and $P(A') = \frac{2}{3}$,then find $P(A' \cap B)$.

Three students $X, Y$ and $Z$ appear for an examination. The probability of $X$ passing the examination is $\frac{1}{5}$,the probability of $Y$ passing the examination is $\frac{1}{4}$ and the probability of $Z$ failing the examination is $\frac{2}{3}$. The probability that at least two of them pass the exam is

An experiment consists of recording the boy-girl composition of families with $2$ children. What is the sample space if we are interested in the number of girls in the family?

If $\frac{1 + 3p}{3}, \frac{1 - p}{4}$ and $\frac{1 - 2p}{2}$ are the probabilities of three mutually exclusive events,then the set of all values of $p$ is