Exercise 10 A library is preparing a display case of books written by faculty members. There are 25 new faculty books, but there is room for only 10 in the display case. Suppose 10 books are selected at random. a. How many different faculty book collections can be displayed (order doesn't matter)? b. If 15 of the new books are written by faculty members from the College of Science and Technology, what is the probability that all 10 displayed books are written by faculty members from this college? Exercise 11 Urn 1 contains three green marbles and three yellow marbles, while Urn 2 contains five green marbles and seven yellow marbles. A marble is drawn at random from Urn 1 and placed in Um 2. A marble is then drawn at random from Um 2. a. Find P(second marble drawn is green). b. Find P(first marble drawn is green | second marble drawn is green). Exercise 12 (Textbook 2.124) A population of voters contains 40% Republicans and 60% Democrats. It is reported that 30% of the Republicans and 70% of the Democrats favor an election issue. A person chosen at random from this population is found to favor the issue in question. Find the conditional probability that this person is a Democrat.Exercise 7 (Textbook 2.149) A large group of people is to be checked for two common symptoms of a certain disease. It is thought that 20% of the people possess symptom A alone, 30% possess symptom B alone, 10% possess both symptoms, and the remainder have neither symptom. For one person chosen at random from this group, find these probabilities: a. The person has neither symptom. b. The person has at least one symptom. c. The person has both symptoms, given that he has symptom B. Exercise 8 Three numbers are chosen at random and without replacement from the numbers (1,2,...,9). What is the probability that the median (i.e. the second largest) number is 4? Exercise 9 (Textbook 2.148) A bin contains three components from supplier A, four from supplier B, and five from supplier C. If four of the components are randomly selected for testing, what is the probability that each supplier would have at least one component tested