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Adults and high school students were asked four trivia questions. The number of correct answers given by each participant was Number of Correct Answers E1 recorded. To the right is a table showing the results. Complete parts a) through d). I) 1 2 3 Al Total Adults 5 32 45 38 36 156 Students 54 14 9 40 41 158 Yotal 59 46 54 78 77 314 a) What is the probability that a randomly selected participant is a student'? (Round to four decimal places as needed.) b) What is the probability that a randomly selected participant had fewer than 2 correct answers? (Round to four decimal places as needed.) c) What is the probability that a randomly selected participant is an adult or had no correct answers? (Round to four decimal places as needed.) d) What is the probability that a randomly selected participant is an adult and had all four correct answers? (Round to four decimal places as needed.) A diamond can be classied as either gem-quality or industrialgrade. Suppose that 97% of diamonds are classied as industrial-grade. (a) Two diamonds are chosen at random. What is the probability that both diamonds are industrial-grade? (b) Eight diamonds are chosen at random. What is the probability that all eight diamonds are industrialgrade? (c) What is the probability that at least one of eight randomly selected diamonds is gem-quality'.7 Would it be unusual that at least one of eight randomly selected diamonds is gem-quality'.7 (a) Two diamonds are chosen at random. What is the probability that both diamonds are industrial-grade? The probability is . (Round to four decimal places as needed.) (b) Eight diamonds are chosen at random. What is the probability that all eight diamonds are industrial-grade? The probability is (Round to four decimal places as needed.) (c) What is the probability that at least one of eight randomly selected diamonds is gem-quality? The probability is . (Round to four decimal places as needed.) Would it be unusual that at least one of eight randomly selected diamonds is gemquality? It would that at least one of eight randomly selected diamonds is gem-quality. not be unusual be unusual When a health survey was conducted in some country. it was found that 78% of the population were infected with a certain virus. 15% were without clean water. and 13% were infected and without clean water. Complete parts a) through c). a) What's the probability that a surveyed person had clean water and was not infected? I (Do not round.) b) Are being infected and being without clean water disjoint? t l A. Yes; some people were infected and were without clean water. ( l B. No; some people were infected but had clean water. (J C. No; some people were infected and were without clean water. (J D. Yes; some people were infected but had clean water. o) Are being infected and being without clean water independent? ( l A. No; ifa person is infected, he or she is more likely to be without clean water. ( l 3. Yes; since the two events are disjoint, they must also be independent. (J C. Yes; infection does not change the probability of being without clean water. (J D. No; if a person is infected, he or she is less likely to be without clean water. Determine whether the events E and F are independent or dependent. Justify your answer. (a) E: A person going into debt. F: The same person having a credit card. [I A. E and F are independent because having a credit card has no effect on the probability ofa person going into debt. C} B. E and F are dependent because going into debt has no effect on the probability of a person having a credit card. a] C. E and F are dependent because having a credit card can affect the probability ofa person going into debt. Ei'i D. E and F are independent because going into debt has no effect on the probability of a person having a credit card. (b) E: A randomly selected person nding cheese revolting. F: A different randomly selected person nding cheese delicious. C} A. E can affect the probability of F, even if the two people are randomly selected, so the events are dependent. a] B. E cannot affect F and vice versa because the people were randomly selected, so the events are independent. 1:] C. E cannot affect F because "person 1 nding cheese revolting" could never occur, so the events are neither dependent nor independent. '2'] D. E can affect the probability of F because the people were randomly selected, so the events are dependent. (c) E: The unusually foggy weather in London on May 8. F: The number of car accidents in London on May 8. [I A. The number of car accidents in London on May 8 could affect the unusually foggy weather in London on May 8, so E and F are dependent. C} B. The unusually foggy weather in London on May 8 could not affect the number of car accidents in London on May 8, so E and F are independent. a] C. The unusually foggy weather in London on May 8 could affect the number of car accidents in London on May 8, so E and F are dependent