The responses of 1024 adults in a certain region to a survey question about the story of Britons' vote to leave the European Union are shown in the accompanying Pareto chart. Find the probability of each event listed in parts (a) through (d) below. |a_l' Click the icon to view the Pareto chart. (a) Randomly selecting an adult who thinks the story is somewhat important Pareto Chart The probability is . (Type an integer or a decimal. Round to three decimal places as needed.) (b) Randomly selecting an adult who thinks the story is not at all important The probability is . (Type an integer or a decimal. Round to three decimal places as needed.) 3' (c) Randomly selecting an adult who thinks the story is not too important or not at all important 8 9 The probability is . (Type an integer or a decimal. Round to three decimal places as needed.) Number responding (d) Randomly selecting an adult who thinks the story is extremely important or very important The probability is . (Type an integer or a decimal. Round to three decimal places as needed.) D E Response Key Extremely important Very important Somewhat important Not too impormnt Not at all important Did not answer In a sample of 1100 U.S. adults, 188 think that most celebrities are good role models. Two US. adults are selected from this sample without replacement. Complete parts (a) through (c). (a) Find the probability that both adults think most celebrities are good role models. The probability that both adults think most celebrities are good role models is E. (Round to three decimal places as needed.) (b) Find the probability that neither adult thinks most celebrities are good role models. The probability that neither adult thinks most celebrities are good role models is :|. (Round to three decimal places as needed.) (c) Find the probability that at least one of the two adults thinks most celebrities are good role models. The probability that at least one of the two adults thinks most celebrities are good role models is |:. (Round to three decimal places as needed.) A probability experiment consists of rolling a 6-sided die. Find the probability of the event below. rolling a number less than 6 The probability is El. (Type an integer or decimal rounded to three decimal places as needed.) In a recent year, about 39% of all infants born in a country were conceived through in-vitro fertilization (IVF). Of the NF deliveries, about twenty-five percent resulted in multiple births. (a) Find the probability that a randomly selected infant was conceived through lVF and was part of a multiple birth. (b) Find the probability that a randomly selected infant conceived through lVF was not part of a multiple birth. (c) Would it be unusual for a randomly selected infant to have been conceived through lVF and to have been part of a multiple birth? Explain. (a) The probability that a randomly selected infant was conceived through lVF and was part of a multiple birth is (Round to the nearest thousandth as needed.) (b) The probability that a randomly selected infant conceived through IVF was not part of a multiple birth is (Round to the nearest thousandth as needed.) (c) Would it be unusual for a randomly selected IVF cycle to result in a pregnancy and produce a multiple birth? Explain. Choose the correct answer below. 0 A. No, this is not unusual because the probability is not less than or equal to 0.05. O B. No, this is not unusual because the probability is less than or equal to 0.05. O C. Yes, this is unusual because the probability is less than or equal to 0.05. O D. Yes, this is unusual because the probability is not less than or equal to 0.05. The percent of college students' marijuana use for a sample of 91 ,135 students is shown in the accompanying pie chart. Find the probability of each event listed in parts (a) through (d) below. K Click the icon to view the pie chart. (a) Randomly selecting a student who never used marijuana The probability is %. . (Round to one decimal place as needed.) Ple Chart (b) Randomly selecting a student who used marijuana Marijuana Use in the Last 30 Days The probability is %. I Never used, 58.2% (Round to one decimal place as needed.) I Used, but not in the last 30 days. 20.0% [I Used 1-9 days, 13.0% E] Used 10-29 days, 6.0% I Used all 30 days, 2.8% (c) Randomly selecting a student who used marijuana between 1 and 29 of the last 30 days The probability is %. (Round to one decimal place as needed.) (d) Randomly selecting a student who used marijuana on at least 1 of the last 30 days The probability is %. (Round to one decimal place as needed.) A stem-and-leaf plot for the number of touchdowns scored by all Division 1A football teams is shown below. Complete (a) If a team is selected at random, nd the probability the team scored at least 30 touchdowns parts (a) through (c). 1 3 4 5 7 8 8 Key: 1'5 = 15 (Round to three decimal places as needed.) 201223457889 3 0 0 1 1 1 2 2 3 3 4 4 5 5 7 7 7 8 9 (b) If a team is selected at random, nd the probability the team scored between 40 and 50 touchdowns inclusive 40012234555567889 5 0 2 3 5 5 7 8 6 1 3 6 7 (Round to three decimal places as needed.) :7 (c) If a team is selected at random, nd the probability the team scored more than 78 touchdowns. (Round to three decimal places as needed.) Are any of these events unusual? Select all the unusual events below. Scoring at least 30 touchdowns is unusual. Scoring between 40 and 50 touchdowns inclusive is unusual. Scoring more than 78 touchdowns is unusual. 99.\"? None of the events are unusual. A probability experiment consists of rolling a fair 10-sided die. Find the probability of the event below. rolling a 10 The probability is E. (Type an integer or decimal rounded to three decimal places as needed.) The table below shows the results of a survey that asked 2858 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts (a) through (d). Frequently Occasionally Not at all Total % Male 228 456 792 1476 Female 207 430 745 1382 Total 435 886 1537 2858 (a) Find the probability that the person is frequently or occasionally involved in charity work. P(being frequently involved or being occasionally involved) =I: (Round to the nearest thousandth as needed.) (b) Find the probability that the person is female or not involved in charity work at all. P(being female or not being involved) = (Round to the nearest thousandth as needed.) (c) Find the probability that the person is male or frequently involved in charity work. P(being male or being frequently involved)= (Round to the nearest thousandth as needed.) (d) Find the probability that the person is female or not frequently involved in charity work. P(being female or not being frequently involved) = (Round to the nearest thousandth as needed.) A study found that people who suffer from obstructive sleep apnea are at increased risk of having heart disease. Identify the two events described in the study. Do the results indicate that the events are independent or dependent? Identify the two events. Choose the correct answer below. 0 A. Sleep apnea and heart disease 0 B. Study and sleep apnea O 0. Study and heart disease 0 D. Having sleep apnea and not having it Are the events independent or dependent? O Dependent 0 Independent The estimated percent distribution of a certain country's population for 2025 is shown in the accompanying pie chart. Find the probability of each event listed in parts (a) through (d) below. I/_' Click the icon to view the pie chart. (a) Randomly selecting someone who is under 5 years old The probability is %. (Round to one decimal place as needed.) National Age Distribution I Under 5 years, 6.4% I 5-14 years, 12.1% [I 1519 years, 5.9% 20-24 years. 6.3% (b) Randomly selecting someone who is 45 years old or over The probability is %. (Round to one decimal place as needed.) (c) Randomly selecting someone who is not 65 years old or over I 25-34 years. 131% _ I 35-44 years, 14.6% The probability is %. I 4564 years, 213% (Round to one decimal place as needed.) I 6574 years, 12.4% I 75 years or over. 7.5% (d) Randomly selecting someone who is between 20 and 34 years old The probability is %. (Round to one decimal place as needed.) By rewriting the formula for the Multiplication Rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B| A) = (A and B) Use the information below to find the probability that a flight arrives on time given that it departed on time. P(A) The probability that an airplane flight departs on time is 0.91. The probability that a flight arrives on time is 0.87. The probability that a flight departs and arrives on time is 0.84. . . . . The probability that a flight arrives on time given that it departed on time is. (Round to the nearest thousandth as needed.)Determine whether the statement is true or false. If it is false, rewrite it as a true statement. If two events are mutually exclusive, they have no outcomes in common. C Choose the correct answer below. 0 A. False. If two events are mutually exclusive, they have some outcomes in common. 0 B. True. 0 C. False. If two events are mutually exclusive, they have every outcome in common. Determine whether the statement is true or false. When an event is almost certain to happen, its complement will be an unusual event. Determine the most appropriate conclusion. 0 A. False, the probability of the complement will have a higher probability than the event. 0 B. False, the complement of an event has an equal probability as the event. 0 C. False, the probability of the complement has no relation to the probability of the event. 0 D. True, the complement would be an unusual event. In a survey of Us. adults with a sample size of 2015. 334 said Franklin Roosevelt was the best president since World War II. Two US. adults are selected at random from this sample without replacement. Complete parts (a) through (d). (8) Find the probability that both adults say Franklin Roosevelt was the best president since World War II. The probability that both adults say Franklin Roosevelt was the best president since World War II is (Round to three decimal places as needed.) (b) Find the probability that neither adult says Franklin Roosevelt was the best president since World War II. The probability that neither adult says Franklin Roosevelt was the best president since World War II is (Round to three decimal places as needed.) (c) Find the probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II. The probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II is (Round to three decimal places as needed.) (d) Which of the events can be considered unusual? Explain. Select all that apply. None of these events are unusual. The event in part (b) is unusual because its probability is less than or equal to 0.05. The event in part (a) is unusual because its probability is less than or equal to 0.05. The event in part (c) is unusual because its probability is less than or equal to 0.05. Determine whether the following events are mutually exclusive. Explain your reasoning. Event A: Randomly select a male communications major. Event B: Randomly select a communications major who is 20 years old. These events V mutually exclusive, since V it is not possible to select a male communications major who is 20 years old. it is possible to select a male communications major who is 20 years old. not all communications majors are male. all communications majors are male. no communications majors are male. every male communications major is 20 years old. not every male communications major is 20 years old. According to a study, 72% of K-12 schools or districts in a country use digital content such as ebooks, audio books, and digital textbooks. Of these 72%, 8 out of 20 use digital content as part of their curriculum. Find the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum. The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is (Round to three decimal places as needed.) A probability experiment consists of rolling a fair 18sided die. Find the probability of the event below. rolling a number divisible by 6 The probability is D. (Type an integer or decimal rounded to three decimal places as needed.) Research has shown that approximately 1 woman in 800 carries a mutation of a particular gene. About 70% of women with this mutation develop skin cancer. Find the probability that a randomly selected Sample Space: Women woman will carry the mutation of this gene and will develop skin cancer. The probability that a randomly selected woman will carry the gene mutation and develop skin cancer is (Round to four decimal places as needed)