Question

a spinner with 8 equal parts numbered 1-8 is spun. are these events mutually exclusive or overlapping?

event a: the spinner lands on a number greater than 6
event b: the spinner lands on 7

mutually exclusive

overlapping

Explanation:

Define the sample space

The spinner has 8 equal parts numbered 1 to 8.

$$ S = \{1, 2, 3, 4, 5, 6, 7, 8\} $$

Identify outcomes for Event A

Using the Overlapping Events knowledge point

$$ A = \{7, 8\} $$

Identify outcomes for Event B

Using the Mutually Exclusive Events knowledge point

$$ B = \{7\} $$

Analyze the intersection of the events

Using the Mutually Exclusive Events and Overlapping Events knowledge points

$$ A \cap B = \{7\} eq \emptyset $$

Determine the relationship

Using the Overlapping Events knowledge point
Since the intersection is non-empty, the events can occur at the same time. Thus, they are overlapping.

Answer:

• mutually exclusive
• overlapping (Correct answer)