Question

A dice is rolled and two events P and Q are given as
P = {1, 4, 3, 5}, Q = {2, 6}

Which of the following describes the relation between P and Q?

• A. Mutually exclusive events
• B. Exhaustive events
• C. Simple events
• D. Compound events

Answer 1

Answer: (A), (B)

Exhaustive events

We will go through the options and check if they describe the relation between P and Q.

A) Mutually exclusive

Two events P and Q are mutually exclusive if $P\cap Q=\varphi$

In our case, $P\cap Q=\{1,4,3,5\}\cap \{2,6\}=\varphi$

$\therefore$ Mutually exclusive

B) Exhaustive P and Q are exhaustive if

$P\cup Q$ = sample space

Here, $P\cup Q=\{1,4,3,5\}\cup \{2,6\}=\{1,2,3,4,5,6\}$

$\therefore$ Mutually exhaustive

C) Simple events do not describe relation between two events.

An event is said to be simple if it has only one outcome

D) Compound events

An event is called a compound event if it has more than one outcome. It does not describe relation between two events. It's defined for a single event.