In a throw of a die, what is the probability of getting a number less than $7$

Two dice are thrown. The events $A,\, B$ and $C$ are as follows:

$A:$ getting an even number on the first die.

$B:$ getting an odd number on the first die.

$C:$ getting the sum of the numbers on the dice $\leq 5$

State true or false $:$ (give reason for your answer)

Statement : $A=B^{\prime}$

The probability of $A, B, C$ solving a problem are $\frac{1}{3},\,\frac{2}{7},\,\frac{3}{8}$ respectively. If all the three try to solve the problem simultaneously, the probability that exactly one of them will solve it, is

A die is thrown, find the probability of following events:  A number greater than or equal to $3$ will appear.

Three coins are tossed once. Find the probability of getting no tails.

An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:

$A:$ the sum is greater than $8$,

$B : 2$ occurs on either die

$C:$ the sum is at least $ 7$ and a multiple of $3.$

Which pairs of these events are mutually exclusive ?