Question

select the correct answer.
joey has a box with 40 football and 120 baseball cards. sylvia has a box with 75 football and 100 baseball cards. joey randomly selects one card from his box, and then sylvia randomly selects a card from her box.
which statement best describes the reason these are independent events?
a. joeys selection of a card has no impact on sylvias cards.
b. sylvia is choosing from a larger group of cards than joey is.
c. joeys and sylvias boxes both contain the same types of cards.
d. joey and sylvia selected their cards randomly.

Explanation:

Step1: Understand independent events

Independent events are events where the outcome of one event does not affect the outcome of another event.

Step2: Analyze each option

• Option A: Joey's selection of a card has no impact on Sylvia's cards. This is correct because Joey is selecting from his box and Sylvia from hers. The two selections are separate and do not influence each other.
• Option B: The size of the group of cards (in terms of quantity) in their boxes is not relevant to the independence of the events. Independence is about the lack of causal or influencing relationship between the two card - selection actions, not about the number of cards.
• Option C: The fact that their boxes contain the same types of cards (baseball and football) is about the nature of the cards (categorically similar), but it doesn't explain independence. Independence is about the non - influencing nature of the two selection processes.
• Option D: Just because they selected their cards randomly does not in itself explain independence. Random selection is a method of selection, but it doesn't clarify why the two events (Joey's selection and Sylvia's selection) are independent.

Answer:

A. Joey’s selection of a card has no impact on Sylvia’s cards.