$A$ die has two faces each with number $1$,three faces each with number $2$,and one face with number $3$. If the die is rolled once,determine $P(2)$.

Three coins are tossed. Describe three events which are mutually exclusive and exhaustive.

From a pack of $52$ cards,one card is drawn at random. The probability that it is either a king or a queen is:

Suppose $A$ and $B$ are two events such that $P(A \cap B) = \frac{3}{25}$ and $P(B - A) = \frac{8}{25}$. Then, $P(B)$ is equal to

$A$ special lottery is to be held to select a student who will live in the only deluxe room available in a hostel. $100$ $III$ year,$150$ $II$ year,and $200$ $I$ year students have applied for the room. Each $III$ year student's name is placed in the lottery $3$ times,each $II$ year student's name $2$ times,and each $I$ year student's name $1$ time. The probability that a $III$ year student gets the room is:

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