Name: Use the following situation to answer questions 1 9: Unit #11 Probability Review A state nonprofit organization wanted to encourage its members to consider the State of New York as a vacation destination. They are investigating whether their online ad campaign influenced its members to plan a vacation in New York within the next year. The organization surveyed its members and found that 75% of them have seen the online ad. 40% of its members indicated they are planning to vacation in New York within the next year, and 15% of its members did not see the ad and do not plan to vacation in New York within the next year. 1. Complete the following hypothetical 1000 two-way frequency table: Watched the online ad Did not watch the online ad Plan to vacation in New York within the next year Do not plan to vacation in New York within the next year Total Total 2. A randomly selected member plans to vacation in New York within the next year. What is the probability the member watched the online ad? 3. What is the probability that a randomly selected member does not plan to vacation in New York within the next year? 4. A randomly selected member watched the online ad. What is the probability the member does not plan to vacation in New York within the next year? 5. A member is selected at random. What is the probability the member watched the online ad or plans to vacation in New York within the year? 6. A member is selected at random. What is the probability the member watched the online ad and plans to vacation in New York within the year?
7. Based on the two-way table, describe two conditional probabilities you could calculate to help decide if members who saw the online ad are more likely to plan a vacation in New York within the next year than those who did not see the ad. 8. Calculate the probabilities you described in Problem 7. 9. Based on the probabilities calculated in Problem 8, do you think the ad campaign is effective in encouraging people to vacation in New York? Explain your answer. 10. A survey conducted at a local high school indicated that 30% of students have a job during the school year. If having a job and being in the 11th grade are not independent, what do you know about the probability that a randomly selected student who is in the 11th grade would have a job? Justify your answer. 11. Eighty percent of the dogs at a local kennel are in good health. If the events a randomly selected dog at this kennel is in good health and a randomly selected dog at this kennel weighs more than 30 pounds are independent, what do you know about the probability that a randomly selected dog that weighs more than 30 pounds will be in good health? Justify your answer.
12. When a player is selected at random from a high school boys baseball team, the probability that he is a pitcher is 0.35, the probability that he is right-handed is 0.79, and the probability that he is a right-handed pitcher is 0.26. Let P be the event that a player is a pitcher, and let R be the event that a player is righthanded. A Venn diagram is provided below. Use the Venn diagram to calculate the probability that a randomly selected player is each of the following. Explain how you used the Venn diagram to determine your answer. a. right-handed but not a pitcher b. a pitcher but not right-handed c. neither right-handed nor a pitcher 13. In contract negotiations between a local government agency and its workers, it is estimated that there is a 50% chance that an agreement will be reached on the salaries of the workers. It is estimated that there is a 70% chance that there will be an agreement on the insurance benefits. There is a 20% chance that no agreement will be reached on either issue. a. Find the probability that an agreement will be reached on both issues. b. Using the Multiplication Rule for Independent Events, determine whether the agreement on salaries and the agreement on insurance are independent events. Justify your answer.
c. Using conditional probability, determine whether the agreement on salaries and the agreement on insurance are independent events. Justify your answer. 14. Odell high offers several sports for girls. Two of them are volleyball and softball. The probability of a girl playing volleyball is 0.56, the probability of playing softball is 0.63 and the probability of playing neither sport is 0.23. Write each using probability notation and find each probability. (You may want to use a Venn diagram or two-way probability table) a) A girl plays both sports b) A girl plays volleyball only c) A girl plays volleyball or softball Let S = girl plays softball, and let V = girl plays volleyball. Write out each of the following using words AND find the probability. Round to the nearest thousandth. e) P(S V) f) P(V S) g) P S h) PV
15. In a school of 320 students, 200 students are on sports teams, and 60 students participate in sports and band, 105 do not participate in either activity. Using a Venn Diagram, determine how many students are involved in either band or sports. 16. The results of a poll of 200 students are shown in the table below: Preferred Music Style Techno Rap Country Female 54 25 27 Male 36 40 18 a. Based on the two-way frequency table above, would you say that being male and preferring country music are mutually exclusive? Explain your answer. b. For this group of students, do these data suggest that gender and preferred music styles are independent of each other? Justify your answer.