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:

Identify the sample space

The spinner has 8 equal parts numbered 1 to 8.

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

List outcomes for Event A

Event A is landing on a number greater than 6.

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

List outcomes for Event B

Event B is landing on 7.

$$ B = \{7\} $$

Determine the intersection of the events

Using the Mutually Exclusive Events and Overlapping Events knowledge points:

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

Since the intersection is not empty, they can occur at the same time.

Answer:

• mutually exclusive
• overlapping (Correct answer)