C1. A computer spam filter is 98% effective at sending spam emails to my junk folder, but will also incorrectly send 1% of legitimate emails to my junk folder. Suppose that 1 in 10 emails are spam. What proportion of emails in my junk folder are actually legitimate emails?

6. Accidents on highways are one of the main causes of death or injury in developing countries and the weather conditions have an impact on the rates of death and injury. In foggy, rainy, and sunny conditions, 1/4, 1/8, and 1/21 of the accidents result in death, respectively. Sunny conditions occur 60% of the time, while rainy and foggy conditions each occur 20% of the time. Given that an accident without deaths occurred, what is the conditional probability that it was foggy at the time?

13. According to Wikipedia, as of November 30, 2019, 43.5% of registered voters in Mercer County are registered democrats (pm = 0.435), and 24.5% of registered voters in Hunterdon County are registered democrats (ph = 0.245). A researcher decides to take an SRS of 45 registered voters in Mercer County and an independent SRS of 45 registered voters in Hunterdon County to investigate, and is surprised when he gets a greater sample proportion of registered democrats in the Hunterdon County sample. Calculate and interpret the probability that the sample proportion of registered democrats in Hunterdon County is greater than the sample proportion of registered democrats in Mercer County. Be sure to show all of your work. (Note- - for those of you wondering why the percentages of registered democrats in the "blue" state of New Jersey are so low, many registered voters in New Jersey do not register with any particular political party)

1.76 Peace Corps Volunteers. The Peace Corps is an indepen- dent U.S. government agency that provides trained volunteers for countries requesting assistance. According to Peacecorps.org, as of September 2012, volunteers currently serve in about 76 different host countries. The average age of a volunteer is about 28 years old. The following table reports the percentage of total volunteers serving by geographic region. Percent of volunteers Region Africa 43% Latin America 21% Eastern Europe/Central Asia 15% Asia 10% Caribbean 4% North Africa/Middle East 4% Pacific Islands 3% a. Use the table to design a procedure for obtaining a stratified sam- ple (with proportional allocation) of 50 Peace Corps volunteers. b. If stratified random sampling with proportional allocation is used to select the sample of 50 Peace Corps volunteers, how many would be selected from the Caribbean?

Human blood is classified by the presence or absence of three main antigens (A, B, and Rh). When a blood specimen is typed, the presence of the A and/or B antigen is indicated by listing the letter A and/or the letter B. If neither the A nor the B antigen is present, the letter O is used.The following table gives the percent of a country's population having each of the eight possible blood types in the sample space. Note that the presence or absence of the Rh antigen is indicated by the symbols + or −, respectively. Blood Types A+ A− B+ B− AB+ AB− O+ O− Percent 35.7 6.1 8.5 1.5 3.4 0.8 37.4 6.6 (a) What is the probability that a person selected at random from the population has a blood type that is type AB given that the person is Rh+? (Round your answer to two decimal places.)(b) What is the probability that a person selected at random from the population has a blood type that is Rh− given that the person is type O? (Round your answer to two decimal places.)

11.27 A forestry official is comparing the causes of forest fires in two regions, A and B. The following table shows the causes of fire for 76 recent fires in these two regions

An interdepartmental task force is being formed to investigate an increase in violent crimes. 1/5 of the task force will be police officers from the local precinct. 1/4 will be ATF agents, and the remaining 22 will be from the FBI. How many people are participating in the task force?

Human blood is classified by the presence or absence of three main antigens (A, B, and Rh). When a blood specimen is typed, the presence of the A and/or B antigen is indicated by listing the letter A and/or the letter B. If neither the A nor the B antigen is present, the letter O is used.The following table gives the percent of a country's population having each of the eight possible blood types in the sample space. Note that the presence or absence of the Rh antigen is indicated by the symbols + or −, respectively. Blood Types A+ A− B+ B− AB+ AB− O+ O− Percent 35.9 6.3 9.5 2.5 3.2 0.8 37.4 4.4 (a) What is the probability that a person selected at random from the population has a blood type that is type A given that the person is Rh−? (Round your answer to two decimal places.)(b) What is the probability that a person selected at random from the population has a blood type that is Rh+ given that the person is type B? (Round your answer to two decimal places.)

Human blood is classified by the presence or absence of three main antigens (A, B, and Rh). When a blood specimen is typed, the presence of the A and/or B antigen is indicated by listing the letter A and/or the letter B. If neither the A nor the B antigen is present, the letter O is used. The following table gives the percent of a country's population having each of the eight possible blood types in the sample space. Note that the presence or absence of the Rh antigen is indicated by the symbols + or -, respectively. 0 Blood Types Percent A+ A 6.3 35.7 B+ B 8.5 1.5 AB+ AB 3.4 0.8 0+ 37.2 (a) What is the probability that a person selected at random from the population has a blood type that is type A given that the person is Rh? (Round your answer to two decimal places.) 6.6 (b) What is the probability that a person selected at random from the population has a blood type that is Rh* given that the person is type B? (Round your answer to two decimal places.)

Human blood is classified by the presence or absence of three main antigens (A, B, and Rh). When a blood specimen is typed, the presence of the A and/or B antigen is indicated by listing the letter A and/or the letter B. If neither the A nor the B antigen is present, the letter O is used.The following table gives the percent of a country's population having each of the eight possible blood types in the sample space. Note that the presence or absence of the Rh antigen is indicated by the symbols + or −, respectively. Blood Types A+ A− B+ B− AB+ AB− O+ O− Percent 35.7 6.1 9.5 1.5 3.4 0.8 37.4 5.6 (a) What is the probability that a person selected at random from the population has a blood type that is type A given that the person is Rh−? (Round your answer to two decimal places.)(b) What is the probability that a person selected at random from the population has a blood type that is Rh+ given that the person is type B? (Round your answer to two decimal places.)