Final answer:
To determine whether events are independent or dependent, we can use the definition of independence. Two events A and B are independent if the probability of A and B occurring together is equal to the product of their individual probabilities. If this equality holds, the events are independent. If not, they are dependent.
Step-by-step explanation:
To determine whether events are independent or dependent, we can use the definition of independence. Two events A and B are independent if the probability of A and B occurring together is equal to the product of their individual probabilities: P(A and B) = P(A) * P(B). If this equality holds, the events are independent. If not, they are dependent.
Here are the determinations for the given events:
a. Being female and preferring basketball: To determine independence, we need more information about the population's preferences. If the probability of being female is independent of the probability of preferring basketball, then the events are independent.
b. Being male and preferring football: Once again, we need more information about the population's preferences. If the probability of being male is independent of the probability of preferring football, then the events are independent.
c. Being female and preferring hockey: Similarly, we need more information about the population's preferences. If the probability of being female is independent of the probability of preferring hockey, then the events are independent.