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 $\leq 5$.
Describe the event $\text{not } B$.

(A) When two dice are thrown,the sample space $S$ contains $36$ outcomes:
$S = \{(x, y) : x, y \in \{1, 2, 3, 4, 5, 6\}\}$.
The event $B$ is defined as getting an odd number on the first die:
$B = \{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6)\}$.
The event $\text{not } B$ (denoted as $B'$) consists of all outcomes in the sample space $S$ that are not in $B$.
Since $B$ contains all outcomes where the first die is odd,$B'$ contains all outcomes where the first die is even.
Therefore,$B' = \{(2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)\}$.
This is equivalent to event $A$.