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 mutual - exclusive definition

Two events are mutually exclusive if they cannot occur at the same time.

Step2: Analyze each option

• Option 1: The number 2 is in a shaded portion. So, landing on an unshaded portion and landing on 2 cannot happen simultaneously.
• Option 2: The number 3 is in an unshaded portion. So, landing on a shaded portion and landing on 3 cannot occur at the same time.
• Option 3: The number 2 is an even - numbered shaded portion. So, landing on a shaded portion and landing on an even number can occur (when landing on 2).
• Option 4: The number 4 is an unshaded number greater than 3. So, landing on an unshaded portion and landing on a number greater than 3 can occur (when landing on 4).
• Option 5: A spinner cannot land on a shaded and an unshaded portion 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