Question

A die is thrown:
P is the event of getting an odd number.
Q is the event of getting an even number.
R is the event of getting a prime number.

Answer 1

Given:
A die is thrown.
Sample space (S) = {1, 2, 3, 4, 5, 6}
∴ n(S) = 6

Now,
P is the event of getting an odd number.
Thus, we have:
P = {1, 3, 5}
∴ n(P) = 3

Q is the event of getting an even number.
Thus, we have:
Q = {2, 4, 6}
∴ n(Q) = 3

R is the event of getting a prime number.
Thus, we have:
R = {2, 3, 5}
∴ n(R) = 3

Here,

$$\begin{gathered} \mathrm{P}\text{'}=\mathrm{S}-\mathrm{P}=\{2,4,6\}=\mathrm{Q} \\ \mathrm{P}\cap \mathrm{Q}=\mathrm{\varphi }\mathrm{and}\mathrm{P}\cup \mathrm{Q}=\{1,2,3,4,5,6\} \end{gathered}$$

Therefore, events P and Q are complementary, mutually exclusive and mutually exhaustive.