Four different letters are to be posted into 6 post boxes. What is the probability that not more than one letter is posted into each of the boxes?

Six persons $A, B, C, X, Y \& Z$ go for an interview. What is the probability of selection of $A$ and $Y$ in the interview?

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 total sum $=7,$ when such a die is rolled twice, is $\frac{13}{96},$ then the value of $x$ is

If $A$ and $B$ are events such that $P\left(A\right)=0.42, P\left(B\right)=0.48$ and $P \left(A \mathrm{and} B\right)=0.16$. Then,

$\mathrm{I}.$ $P \left(\mathrm{not} A\right)=0.58$

$\mathrm{II}.$ $P \left(\mathrm{not} B\right)=0.52$

$\mathrm{III}.$ $P \left(A \mathrm{or} B\right)=0.47$

In a college, $\frac{1}{5}th$ of the girls and $\frac{1}{8}\mathrm{th}$ of the boys took part in a social camp. The total number of students in the college took part in the camp is:

For the following distribution function $F\left(x\right)$ of a random variable $X$

$P \left(3<X \le 5\right)=$