Final answer:
Hermione must be 30 years old or over to enter the competition, so the correct inequality is A ≥ 30. The statements about sports, skiing, and snowboarding related to age groups involve probabilities and some are incorrect in the context provided, especially without additional information.
Step-by-step explanation:
To answer the student's question about Hermione's age and the eligibility for the music competition: To enter a music competition, you must be 30 years old or over. Hermione is A years old and she enters the competition. The correct inequality to represent this situation is C. A ≥ 30, which means Hermione's age A is greater than or equal to 30 years old.
Now, let's look at the statements provided:
- A. Sport and age are independent events: This could be true or false depending on the context, but in general, being interested in a sport and being of a certain age are not necessarily dependent on each other.
- B. Ski and age 11-20 are mutually exclusive events: This is false. Being in the age group of 11-20 does not prevent a person from skiing.
- C. P(Ski AND age 21–40) < P(Skilage 21-40): This statement is incorrect. This seems to be a misunderstanding of probability notation. P(Ski|age 21-40) refers to the probability of skiing given that the person is aged 21-40, not the probability of skiing and being aged 21-40 at the same time.
- D. P(Snowboard OR age 0-10) < P(Snowboard|age 0-10): This is also false. The probability of snowboarding or being age 0-10 is likely to be higher than the conditional probability of snowboarding given that the person is age 0-10.