Statistics 101 Problem Set # 3 Due Monday November 1st 1. Ex 4.24 page 2502. Ex 4.36 page 2533a. Ex 4.54 page 277 b. Ex 4.55 page 2774. Ex 5.40 page 333 5. Team A is a better baseball team than Team B in that the probability that Team A wins each game is .6. However, if Team A wins a game the chance that Team A wins the next game increases to .7. a) What is the probability that Team A wins at least one of the two games?b) Team A and Team B are now in a seven game world series. Team A won game 5 and leads in the series three games to two so that there are at most two games remaining. i) Write down the sample space for what can happen in the remaining game(s). ii) Write down the probability for each point in the sample space. If there is a game 7 assume that the probability that Team A wins or loses only depends on the outcome of game 6 and not on what happened on previous games. iii) What is the probability that Team A wins the series? iv) If Team A wins the series, what is the probability that the series went seven games?6. A drug company has a new anti-hypertensive drug. It has three possible positionings for the new drug that it is considering: Pl: Direct the effort to all physicians P2: Direct the effort only to physicians who are internists. P3: Direct the effort only to physicians who are cardiologists. The success of each positioning depends on whether a competitor will launch a new drug or not over the course of the year. The following information is given: i) If the competitor launches the new drug over the course of the year then the profits willbe 30,50, and 60 million if P1, P2, and P3 are the positionings, respectively. ii) If the competitor does not launch the new drug, then the profits will be 90, 80 and 60 million if P1, P2, and P3 are the positionings, respectively. iii) There is a 60% chance that the new drug will be not launched by the competitor this year. iv) If the company waits six months to promote the drug, then it will get either a positive or negative indication as to whether the competitor's drug will be launched. The probability of a positive indication is 3/4 if the competitor's drug will ultimately be launched. The probability of a negative indication is 2/3 if the competitor's drug will not be launched.a) If the company employs one of the positionings now, which one is the best in terms of maximizing expected profit? b) The company decides to wait six months and receives a positive indication that the competitor’s drug will be launched. What is the probability that the new drug will be launched by the competitor?c) If the company employs one of the positionings after six months and receives a positive indication, which positioning is best in terms of maximizing expected profit?d) What is the expected value of profit if the company waits six months before promotingthe drug? Note: You need to take into account the chances of positive and negative indications and the best positions for each of these two cases. 7. Extra Credit In a population of people some have blue eyes and other do not. In order to study the genetics of eye color, the following information is collected on mother’s, father’s and first born child’s eye color:i) ¼ of all mothers have blue eyes and ¼ of all fathers have blue eyes.ii) ¼ of all children have blue eyes.iii) Fathers and mothers marry independent of eye color. Hence there is a 1/16th chance that a family has both parents with blue eyes.iv) In all families where both parents have blue eyes, the child also has blue eyes.v) 1/3 of the children have blue eyes in families where the mother’s eyes are blue and the father’s eyes are not blue.vi) 1/3 of the children have blue eyes in families where the father’s eyes are blue and the mother’s eyes are not blue.a) What is the probability that at least one parent’s eye color is blue?b) What is the probability that at least one of the three people (father, mother and child) does not have blue eyes?c) What is the probability that the child has blue eyes if neither parent has blue eyes?d) What is the probability that at least one of the parents eye color is blue if the child’s eye color is