1. Suppose that of all individuals buying a certain digital camera, 60% include an optional memory card, 40% include an extra battery, and 30% include both a card and a battery. Given that a randomly selected person purchased an extra battery, what is the probability that an optional memory card was also purchased? 2. Samples of a metallic part are classified on the basis of surface nish and length measurements. The results are summarized as follows: Excellent Length Good Length I Excellent Surface Finish \" Good Surface Finish Let A be the event the sample has excellent length and let B denote the event sample has excellent surface finish. Determine [8) P04) {b} P(B' n A') it) P(A|B) {d} Are A, 3 independent events? Justify your answer. 3. According to Opinion Dynamics Poll, 54% of adult men and 33% of adult women believe in aliens. It is known that 48% of the population are men. What percentage of adults believe in aliens? 4. According to the American Lung Association, 7% of the population has lung disease. 0fthose having lung disease, 90% are smokers; and of those not having lung disease, 25% are smokers. What is the probability that a smoker has lung disease