Question

Consider a single spin on the spinner shown below.

A circle is split into sections 1, 2, 4, and 3. A spinner is pointing at number 2. Sections 1 and 2 are shaded.

Which events are mutually exclusive? Check all that apply.

landing on an unshaded portion and landing on 2
landing on a shaded portion and landing on 3
landing on a shaded portion and landing on an even number
landing on an unshaded portion and landing on a number greater than 3
landing on a shaded portion and landing on an unshaded portion

Answer 1

Mutually exclusive means the two events cannot happen on the same spin (their intersection is empty).

Shaded = {1,2}; Unshaded = {3,4}; 2 = {2}; 3 = {3}; even = {2,4}; >3 = {4}.

- Unshaded and 2: {3,4} ∩ {2} = ∅ → mutually exclusive.
- Shaded and 3: {1,2} ∩ {3} = ∅ → mutually exclusive.
- Shaded and even: {1,2} ∩ {2,4} = {2} → not mutually exclusive.
- Unshaded and >3: {3,4} ∩ {4} = {4} → not mutually exclusive.
- Shaded and unshaded: {1,2} ∩ {3,4} = ∅ → mutually exclusive.

So the mutually exclusive pairs are 1, 2, and 5.