Question

which of these are non-overlapping events?

a.) drawing a black card and drawing a 7 from a standard deck of cards

b.) drawing a red card and drawing a six of clubs from a standard deck of cards

c.) drawing a black card and drawing an ace of spades from a standard deck of cards

d.) drawing a face card and drawing a queen from a standard deck of cards

Explanation:

Define non-overlapping events

Non-overlapping (mutually exclusive) events cannot occur at the same time. For two events \(A\) and \(B\), they are non-overlapping if their intersection is empty:

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

Analyze each option

• Option a: A card can be both black and a 7 (the 7 of spades or 7 of clubs). These events overlap.
• Option b: A card cannot be both red and the six of clubs, because clubs are always black. These events do not overlap.
• Option c: A card can be both black and the Ace of spades. These events overlap.
• Option d: A card can be both a face card and a Queen. These events overlap.

Identify the correct choice

Since the events in option b cannot occur simultaneously, they are non-overlapping.

Answer:

• a.) Drawing a black card and drawing a 7 from a standard deck of cards
• b.) Drawing a red card and drawing a six of clubs from a standard deck of cards (Correct answer)
• c.) Drawing a black card and drawing an Ace of spades from a standard deck of cards
• d.) Drawing a face card and drawing a Queen from a standard deck of cards