Researchers are interested in the relationship between cigarette smoking and lung cancer. Suppose that an adult male is randomly selected from a particular population. The following table shows the probabilities of some events related to this chance process:Find the probability that the individual gets cancer given that he is a smoker.

(b) Find the probability that the individual smokes OR gets cancer. Show your work.

(c) Suppose that you are trying to prove that smoking and getting cancer are independent events. If this is indeed the case, what would the value of the probability of "Gets Cancer" (shown by ??? in the table) need to be for the two events to be independent? Show work/explain.