Question

The events {1}, {2}, {3, 4}, {5}, {6} are mutually exclusive and exhaustive when we throw a die

• A. True
• B. False

Answer 1

The correct option is A

True

We know the sample S associated with throwing a die

S = {1, 2, 3 4, 5, 6}

We say two events are mutually exclusive if they have no outcome in common or $A\cap B=\varphi$.

For more than two events to be mutually exclusive each pair should be mutually exclusive. We are given five events {1}, {2}, {3, 4}, {5}, {6}

None of them have any element in common. It means they are mutually exclusive.

We say a set of events $E_1,E_2,E_3\dots E_n$ is exhaustive, if their combination gives sample space S.

i.e., $E_1\cup E_2\cup E_3\dots E_n=S$

Here, $\left\{1\right\}\cup \left\{2\right\}\cup \{3,4\}\cup \left\{5\right\}\cup \left\{6\right\}$

= {1, 2, 3, 4, 5, 6} = S

$\Rightarrow$ Exhaustive

$\Rightarrow$ They are mutually exclusive and exhaustive.