According to a study done in the United Kingdom, a male’s probability of death from lung cancer during his lifetime is 0.077. For someone that is a heavy smoker (at least 25 cigarettes a day), that probability goes up to 0.244. (For someone who has never smoked, that probability goes down to 0.002.) We will let C represent the event a male dies of cancer and S represent the event that a person is a heavy smoker. 

a. Using probability notation, define the two probabilities (0.077 and 0.244) given above. 

b. Are smoking and dying of lung cancer independent? Explain why or why not, based on the probabilities given.