Question

a coin is drawn from a hat with 6 pennies, 4 dimes, and 5 quarters. are these events mutually exclusive or overlapping?

event a: the coin drawn has a value \\(\ge 10\\) cents
event b: the coin drawn is a quarter

mutually exclusive

overlapping

Explanation:

Identify the outcomes for each event

Using the Mutually Exclusive Events and Overlapping Events knowledge points

• Event A (value \(\ge 10\) cents): The coin drawn must be a dime (10 cents) or a quarter (25 cents).
• Event B (coin is a quarter): The coin drawn must be a quarter.

Determine if the events overlap

Using the Overlapping Events knowledge point

• The outcome "drawing a quarter" satisfies both Event A and Event B.
• Since the two events share a common outcome, they can occur at the same time.
• Therefore, the events are overlapping.

Answer:

• mutually exclusive
• overlapping (Correct answer)