Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that both cards are spades? Are these events independent?

1/17; no, they are dependent events

1/16; yes, they are independent eventssg

25/52; yes, they are independent events

3/52; no, they are dependent events

A recent survey by the American Cancer Society shows that the probability that someone is a smoker is P(S) = 0.19. It has also determined that the probability that someone has lung cancer, given that he or she is a smoker, is P(LC|S) = 0.158. What is the probability (rounded to the nearest hundredth) that a random person is a smoker and has lung cancer P(S LC)?

0.03

0.83

0.35

0.02

At a high school, the probability that a student takes a science class and a history class is 0.48. The probability that a student takes a science class is 0.82, and the probability that the student takes a history class is 0.64. What is the probability (rounded to the nearest hundredth) that a student takes a history class given that the student is taking a science class?

0.39

0.75

0.30

0.59