Question

consider a single spin of the spinner. which events are mutually exclusive? select two options. landing on a shaded portion and landing on an even number landing on a shaded portion and landing on a number greater than 3 landing on a shaded portion and landing on a 3 landing on an unshaded portion and landing on an odd number landing on an unshaded portion and landing on a number less than 2

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: Landing on a shaded portion and landing on an even number. The number 4 is shaded and even, so they are not mutually exclusive.
• Option 2: Landing on a shaded portion and landing on a number greater than 3. The number 4 is shaded and greater than 3, so they are not mutually exclusive.
• Option 3: Landing on a shaded portion and landing on a 3. The number 3 is un - shaded, so a spin cannot land on a shaded portion and 3 simultaneously. These two events are mutually exclusive.
• Option 4: Landing on an unshaded portion and landing on an odd number. The number 3 is unshaded and odd, so they are not mutually exclusive.
• Option 5: Landing on an unshaded portion and landing on a number less than 2. The number 1 is unshaded and less than 2, so they are not mutually exclusive.

Answer:

Landing on a shaded portion and landing on a 3; Landing on an unshaded portion and landing on a number less than 2