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:

Analyze the spinner outcomes

The spinner is divided into four equal sectors labeled 1, 2, 3, and 4.

• Shaded sectors: 1 and 4
• Unshaded sectors: 2 and 3
• Even numbers: 2 and 4
• Odd numbers: 1 and 3

Define mutually exclusive events

Using the Mutually Exclusive Events knowledge point
Two events are mutually exclusive if they cannot occur at the same time. In other words, their intersection is empty:

$$ P(A \cap B) = 0 $$

Evaluate each option

• Option 1: "landing on a shaded portion and landing on an even number"
• Shaded sectors: \(\{1, 4\}\)
• Even sectors: \(\{2, 4\}\)
• Intersection: \(\{4\}\) (not mutually exclusive)

• Option 2: "landing on a shaded portion and landing on a number greater than 3"
• Shaded sectors: \(\{1, 4\}\)
• Number greater than 3: \(\{4\}\)
• Intersection: \(\{4\}\) (not mutually exclusive)

• Option 3: "landing on a shaded portion and landing on a 3"
• Shaded sectors: \(\{1, 4\}\)
• Landing on 3: \(\{3\}\)
• Intersection: \(\emptyset\) (mutually exclusive)

• Option 4: "landing on an unshaded portion and landing on an odd number"
• Unshaded sectors: \(\{2, 3\}\)
• Odd sectors: \(\{1, 3\}\)
• Intersection: \(\{3\}\) (not mutually exclusive)

• Option 5: "landing on an unshaded portion and landing on a number less than 2"
• Unshaded sectors: \(\{2, 3\}\)
• Number less than 2: \(\{1\}\)
• Intersection: \(\emptyset\) (mutually exclusive)

Answer:

• 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 (Correct answer)
• landing on an unshaded portion and landing on an odd number
• landing on an unshaded portion and landing on a number less than 2 (Correct answer)