Exercise 1. A club has 15 registered members of whom 8 are women and 7 are men. A group photo of all members is to be taken sitting in a row. The seats are assigned randomly. a) What is the probability that no two women and no two men are sitting side by side (i.e. women and men are sitting in alternate seats)? (4pt) b) What is the probability that all men are sitting together? (4pt) Exercise 2. A public health researcher examines the medical records of a group of 1114 men who died in 1995 and discovers that 300 of the men died from causes related to heart disease. Moreover, 316 of the 1114 men had at least one parent who suffered from heart disease, and, of these 316 men, 159 died from causes related to heart disease. Calculate the probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease. (8pt) Exercise 3. There are 3 red and 2 blue balls in box I, and 1 red and 2 blue balls in box II. Two balls are randomly selected from box I and placed into box II. Next two balls are drawn from box II and it turns out that the selected balls are of different colours. Given this information, what is the conditional probability that two balls of same colours were transferred from box I to box II? (10th Exercise 4. Suppose there is 65% probability that one will encounter a red light in a traffic signal. a) Find the probability that you will have to stop in a red light at least once during the work week? Here \"work week\" starts on Monday and ends on Friday (inclusive). (2pt) b) What is the probability that in a certain work week, you will be stopped at the traffic signal first time on Thursday? (2pt) You can assume that getting a red signal on any day is independent of other days