Final answer:
Being a girl and playing a sport are dependent events in both given scenarios, as the probabilities P(Girl) and P(Girl| plays a sport) are not equal, indicating that one event affects the probability of the other.
Step-by-step explanation:
To determine whether two events are independent, we can use the definition that two events, A and B, are independent if and only if the probability of A given B is equal to the probability of A, that is, P(A|B) = P(A).
For the student's question, we ascertain whether being a girl (event G) and playing a sport (event S) are independent events by checking if P(G|S) equals P(G). We have two scenarios:
- Scenario A: P(G) = 0.49 and P(G|S) = 0.44. Since these probabilities are not equal, G and S are not independent.
- Scenario B: P(G) = 0.49 and P(G|S) = 0.62. Again, because these probabilities are not equal, G and S are not independent.
In conclusion, in both scenarios, being a girl and playing a sport are dependent events since knowledge of one event does affect the probability of the other event occurring.