Question

consider a single spin on the spinner shown below. 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

Explanation:

Step1: Recall the definition of mutually - exclusive events

Mutually - exclusive events are events that cannot occur at the same time.

Step2: Analyze each option

• Option 1: landing on an unshaded portion and landing on 2

Portion 2 is shaded. So, a spin cannot land on an unshaded portion and on 2 simultaneously.

• Option 2: landing on a shaded portion and landing on 3

Portion 3 is unshaded. So, a spin cannot land on a shaded portion and on 3 simultaneously.

• Option 3: landing on a shaded portion and landing on an even number

Portion 2 is shaded and 2 is an even number. So, these two events can occur at the same time.

• Option 4: landing on an unshaded portion and landing on a number greater than 3

Portion 4 is unshaded and 4>3. So, these two events can occur at the same time.

• Option 5: landing on a shaded portion and landing on an unshaded portion

A portion cannot be both shaded and unshaded. So, these two events cannot occur at the same time.

Answer:

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 unshaded portion