7. Smokers. (10 points) According to the Center for Disease Control (CDC), \"Compared to nonsmokers, men who smoke are about 23 times more likely to develop lung cancer and women who smoke are about 13 times more likely.\" The CDC also states that roughly 15% of all women are smokers, 18% of all adults are smokers. Assume that half the adults are women. (a) If you learn that a woman has been diagnosed with lung cancer, and you know nothing else about her, what is the probability she is a smoker? (b) What fraction of adult smokers in the USA are women? Hint: Let A be the event that \"a woman smokes,\" and B be the event that \"a woman gets cancer.\