Question

(a) list an example of two events that are independent. choose the correct answer below.

a. rolling a die twice
b. selecting a queen from a standard deck, not replacing it, and then selecting a queen from the deck
c. not putting money in a parking meter and getting a parking ticket
d. a father having hazel eyes and a daughter having hazel eyes

Explanation:

Define independent events

Using the Independent Events Probability knowledge point
Two events are independent if the occurrence of one event does not affect the probability of the occurrence of the other event.

Analyze the given options

Using the Independent Events Probability and Dependent Events knowledge points

• Option A: Rolling a die twice. The outcome of the first roll has absolutely no influence on the outcome of the second roll. The probability of rolling any number remains \(\frac{1}{6}\) for both rolls. Thus, these events are independent.
• Option B: Selecting a queen from a deck, not replacing it, and selecting another queen. Since the first card is not replaced, the total number of cards and the number of queens change, which alters the probability of the second draw. These are dependent events.
• Option C: Not paying a parking meter and getting a ticket. Failing to pay directly increases the probability of receiving a ticket. These are dependent events.
• Option D: A father and daughter both having hazel eyes. Genetics are passed down, so the father's eye color directly influences the probability of the daughter's eye color. These are dependent events.

Answer:

• A. Rolling a die twice (Correct answer)
• B. Selecting a queen from a standard deck, not replacing it, and then selecting a queen from the deck
• C. Not putting money in a parking meter and getting a parking ticket
• D. A father having hazel eyes and a daughter having hazel eyes