Question

Are being a girl and playing a sport independent events?

a) Yes, they are independent, because P(girl) = 0.49 and P(girl| plays a sport) = 0.44.
b) No, they are not independent, because P(girl) = 0.49 and P(girl| plays a sport) = 0.62.
c) Yes, they are independent, because P(girl) < 0.49 and P(girl| plays a sport) = 0.62.
d) No, they are not independent, because P(girl) = 0.49 and P(girl plays a sport) = 0.44.

Answer 1

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.