4. W.I.E. Gates wrote, \"Then there is the man who drowned crossing a stream with an average depth of six inches.\" How is that possible? 6. In a certain city, 55.6% of the residents are male or colorblind. 0.1% of the residents are both male and colorblind. 55.2% of the residents are male. (a) What percentage of the residents is colorblind? (b) What percentage of the residents is female and not colorblind? (c) What percent of the males is colorblind? (d) What percent of the colorblind is male? (e) What percent of the females is not colorblind? (f) Are the event of being male and the event of being colorblind mutually exclusive? Justify your answer by showing some calculations. (g) Are the event of being male and the event of being colorblind dependent? Justify your answer by showing some calculations. Show your work to receive full credit. (You may use a rule of probability or draw a Venn diagram.) . Toss two dice. Let rv X be the absolute difference (i.e., never negative) between the upturned faces. You should see that the smallest value of X is 0,: the largest value is 5. Write SAS code to determine the probability distribution of X. (a) Write the probability distribution of X. (That is, I need to see the table below consisting of the possible values of X and below each value, write the probability.) :1: 01i2i3'4i5 P[X=:r] \\ i i (b) Write SAS code to draw the probability histogram. Attach the histogram to your home- work. What is the shape of the distribution? (c) Find the mean and variance of the probability distribution. (d) Are the outcomes equally probable? You and your friends are asked to predict the value of the absolute difference between the upturned faces of two dice. What value will you bet on? . The in-hospital mortality rate for 16 clinical conditions at 981 hospitals was published in Shortell 8: Hughes (1988). It was reported that in-hospital mortality was 10.5% for coronary-bypass. Suppose an institution changes from an academic institution to a private for-prot institution. They find that after the change, of the rst 20 patients receiving coronary-bypass surgery, 5 die. Assume this hospital is representative of the total pool of 981 hospitals. (a) What is the probability that, of 20 patients receiving coronary-bypass surgery, exactly 5 will die in-hospital? (b) What is the probability of at least 5 deaths among the coronary-bypass patients? (c) What is the probability of no more than 5 deaths among the coronary-bypass patients? 4.14 Cardiovascular Hospitalizations. From the Florida State Center for Health Statistics report Women and Cardiovascular Disease Hospitalization, we obtained the following table show- ing the number of female hospitalizations for cardiovascular dis- ease, by age group, during one year. Age group (yr) Number 019 810 2039 5,029 4049 10,977 5059 20,983 6069 36,884 7079 65,017 80 and over 69,167 One of these case records is selected at random. Find the proba- bility that the woman was a. in her 50s. b. less than 50 years old. c. between 40 and 69 years old, inclusive. d. 70 years old or older. 160 For one of these woman selected at random, let Here, for example, HTIH represents the outcome that the rst toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes constituting each of the following four events. A = event exactly two heads are tossed, B = event the rst two tosses are tails, C = event the rst toss is heads, D = event all four tosses come up the same. 4.45 Dice. Refer to Exercise 4.41. For each of the following events, list the outcomes that constitute the event and describe the event in words. a. (not A) b. (A & B) c. (B or C) CHAPTER 4 Probability Concepts 4.50 Family Planning. The following table provides a fre- quency distribution for the ages of adult women seeking preg- nancy tests at public health facilities in Missouri during a 3-month period. It appeared in the article \"Factors Affecting Contraceptive Use in Women Seeking Pregnancy Tests\" (Family Planning Perspectives, Vol. 32, No. 3, pp. 124131) by M. Sable et a1. Age (yr) Frequency 1819 89 2024 130 2529 66 3039 26 the number of rooms in U.S. housing units. The frequencies are in thousands. A = event the woman is at least 25 years old, B = event the woman is at most 29 years old, C = event that the woman is between 18 and 29 years old, and D = event that the woman is at least 20 years old. Describe the following events in words, and determine the num- ber of outcomes (women) that constitute each event. a. (not D) b.(B&D) c.(CorA) d.(A&B) Rooms No. of units 1 637 2 1,399 3 10,941 4 22,774 5 28,619 6 25,325 7 15,284 4.160 AIDS by Drug Injection. The Centers for Disease Con- trol and Prevention publishes selected data on AIDS in the doc- ument HIV/AIDS Surveillance Report. The rst two columns of the following table provide a race/ethnicity distribution for males in the United States and its territories who are living with AIDS; the third column gives, for each race/ethnicity category, the per- centage of those who were exposed to AIDS by drug injection. 9. m... .......... Race/ethnicity White, not Hispanic 12.4 Black, not Hispanic 21.8 Hispanic 23.6 Asiaanacic Islander 11.6 Native American 18.5 a. Determine the percentage of males living with AIDS who are Hispanic and were exposed by drug injection. b. Determine the percentage of males living with AIDS who were exposed by drug injection. 1:. Of those White, not Hispanic males living with AIDS, what percentage were exposed by drug injection? (1. Of those males living with AIDS who were exposed by drug injection, what percentage are White, not Hispanic