Conditional Probability and Independence

What is the probability that a randomly selected student plays sports and does not participate in community service?

What is the probability that a randomly selected student plays sports given that they do not do community service?

What is the probability that a randomly selected student does not do community service if they do not play sports?

What is the probability that a student plays sports given that they do community service?

Are the events "Sports" and "Community Service" independent?

• Yes, because P(S) is the same as P(S|CS).

• No, because P(S) is not the same as P(S|CS).

• Yes, because P(S) is the same as P(CS|S).

• No, because P(S) is not the same as P(CS|S).

• What is the probability of a student who does community service and does not play sports?

• What is the probability of a student who does community service given that they do not play sports?

• What is the probability of a student who does not play sports given that they do not do community service?

• What is the probability of a student who does not play sports or does not do community service?

What is the probability that a randomly selected student is not in a club?

What is the probability that a student takes Latin given that they participate in a club?

What is the probability that a student does not participate in a club given that they take sign language?

Are the events "takes Spanish" and "participates in a club" independent events?

• Yes, because P(S) is the same as P(S|C).

• No, because P(S) is not the same as P(S|C).

• Yes, because P(S) is the same as P(C|S).

• No, because P(S) is not the same P(C|S).