PLEASE ADRESS ALL THE QUESTIONS

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AP Statistics Ch 5 Aim 4; Conditional Probability Problems Page 5 of 5 ework #52 van's Statistics: Informed Decisions Using Data Read pages 296-299 em 1: Asia has become a major competitor of the United States and Western Europe in education as well as economics. Here are the counts of first university degrees conferred in science and engineering in the three regions: United Western Field States Europe Asia Total Engineering 61,941 158,931 280,772 501,644 Natural Science 111,158 140,126 242,879 494,163 Social Science 182,166 116,353 236,018 . 534,537 Total 355,265 415,410 759,669 1,530,344 Give answers correct to three decimal places A. Find the probability that the degree conferred was in engineering. B. Find the probability that the degree conferred was in engineering, given that the region was Asia. C. Are the events "degree in engineering" and "Asia" independent? Explain. D. Find the probability that the region was the United States, given that the degree conferred was in social science. E. Are the events "United States" and "degree in social science" independent? Explain. F. Find the probability that the degree conferred was in natural science or social science. G. Find the probability that the degree conferred was in engineering or the region was the United States. H. Find the probability that the degree conferred was in the social science and the region was Asia.AP Statistics Ch 5 Aim 4; Conditional Probability Problems Page 5 of 5 ework #52 van's Statistics: Informed Decisions Using Data Read pages 296-299 em 1: Asia has become a major competitor of the United States and Western Europe in education as well as economics. Here are the counts of first university degrees conferred in science and engineering in the three regions: United Western Field States Europe Asia Total Engineering 61,941 158,931 280,772 501,644 Natural Science 111,158 140,126 242,879 494,163 Social Science 182,166 116,353 236,018 . 534,537 Total 355,265 415,410 759,669 1,530,344 Give answers correct to three decimal places A. Find the probability that the degree conferred was in engineering. B. Find the probability that the degree conferred was in engineering, given that the region was Asia. C. Are the events "degree in engineering" and "Asia" independent? Explain. D. Find the probability that the region was the United States, given that the degree conferred was in social science. E. Are the events "United States" and "degree in social science" independent? Explain. F. Find the probability that the degree conferred was in natural science or social science. G. Find the probability that the degree conferred was in engineering or the region was the United States. H. Find the probability that the degree conferred was in the social science and the region was Asia.AP Statistics Ch 5 Aim 4; Conditional Probability Problems Page 5 of 5 ework #52 van's Statistics: Informed Decisions Using Data Read pages 296-299 em 1: Asia has become a major competitor of the United States and Western Europe in education as well as economics. Here are the counts of first university degrees conferred in science and engineering in the three regions: United Western Field States Europe Asia Total Engineering 61,941 158,931 280,772 501,644 Natural Science 111,158 140,126 242,879 494,163 Social Science 182,166 116,353 236,018 . 534,537 Total 355,265 415,410 759,669 1,530,344 Give answers correct to three decimal places A. Find the probability that the degree conferred was in engineering. B. Find the probability that the degree conferred was in engineering, given that the region was Asia. C. Are the events "degree in engineering" and "Asia" independent? Explain. D. Find the probability that the region was the United States, given that the degree conferred was in social science. E. Are the events "United States" and "degree in social science" independent? Explain. F. Find the probability that the degree conferred was in natural science or social science. G. Find the probability that the degree conferred was in engineering or the region was the United States. H. Find the probability that the degree conferred was in the social science and the region was Asia.8) 8) Find the probability of correctly answering the first 2 questions on a multiple choice test if random guesses are made and each question has 6 possible answers. A) 3 B ) D) 9) 9) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a King and the second card is a queen. Express Your 3.MIT JUM answer as a simplified fraction. A) - B) -2 102 9363 D) 6:63 dong balsolbel sell bold Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted. 10) The table below describes the smoking habits of a group of asthma sufferers. 10) Light Heavy Nonsmoker smoker smoker Total Men 351 85 68 524 adade lamco ,noideaup all mwenA Women 370 71 60 501 Total 721 156 148 1025 If one of the 1025 subjects is randomly selected, find the probability that the person chosen is a woman given that the person is a light smoker. Round to the nearest thousandth. A) 0.069 B) 0.455 C) 0.142 D) 0.252 Solve the problem. 11) 8 basketball players are to be selected to play in a special game. The players will be selected from a 11) list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest players will be selected? A 2.220,075 B) 7 213,127,200 D) 40.320 12) In a certain lottery, five different numbers between 1 and 38 inclusive are drawn. These are the 12) winning numbers. To win the lottery, a person must select the correct 5 numbers in the same order in which they were drawn. What is the probability of winning? 1 A) 120 B) - 120 60.233,040 80.233,040 D) 38 Provide an appropriate response. 13) In a game, you have a 1/39 probability of winning $91 and a 38/39 probability of losing $7. What is 1 your expected value? A) $2 33 B) $9.15 C)-56.82 D) -$4.49 Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. 14) n = 64, x = 3, p= 0.04 14) A) 0.375 B) 0.139 9 0.091 D) 0.221Bayesian Spam Filters Suppose have received 5 emails and categorized each of them as either spam or ham (any email that is not spam is ham). The results are displayed below in the table. Use this information to answer the following questions. You should input your answers in decimal form, rounded to the nearest thousandth. For example, if you find 0.0148 as an answer, you should enter '0.015". Email 1 Email 2 Email 3 Email 4 Email 5 spam spam spam ham ham buy money nigeria money car profit bank bank home nigeria home check home nigeria profit wire car Part A. Based on the data above, estimate the probability of an arbitrary email being spam, p(spam). Based on the data above, estimate the probability of an arbitrary email being ham, p(ham)- Part B. Given that you know an email is spam, estimate the probability that it contains the word "nigeria". (That is, estimate p(nigeria | spam)) Given that you know an email is ham, estimate the probability that it contains the word "nigeria". (That is, estimate p(nigeria | ham)) Part C. As discussed in class, we can categorize an email by comparing p(ham | email) to p(spam | email), and classifying the given email according to which quantity is larger. In general, these conditional probabilities are estimated using Bayes' Rule as p(category | email) = P(email [ category)p(category) p(email) We note that for both the spam and ham computations, the denominator in this fraction is the same, and thus we can instead classify the email according to which numerator is larger. Compute the estimated numerator for p(spam | nigeria). Compute the estimated numerator for p(ham | nigeria). Part D. Based on your work above, would our spam filter classify an email containing solely the word "nigeria' as ham or spam? Note: Make sure to double-check your answers for Part C before making a selection!Suppuse We llave wie IViewing PIVvauIly distribution: P(x) 0 0.041 1 0.025 2 0.25 3 0.309 4 0.375 Would it be considered unusually low to have a result of x = 1? Read the answers carefully, as they are very similar. ONo, because the probability of obtaining x = 1 is less than 0.05. ONo, because the probability of obtaining x = 1 is more than 0.05. ONo, because the probability of obtaining x = 0 or x = 1 is more than 0.05. OYes, because the probability of obtaining x = 1 is less than 0.05. ONo, because the probability of obtaining x = 0 or x = 1 is less than 0.05. OYes, because the probability of obtaining x = 0 or x = 1 is less than 0.05.WORKSHEET FOR PROBABILITY LAB Instructions: Answer the following questions by writing the appropriate today. answers in the blanks provided. Turn in the worksheet before leaving class A 1 child? 1. If two parents are Aa and Aa, what is the probability that they have a homozygous a. 1 b. 3/4 (91/2 d. 1/4 e. 1/B 1. C 2. You have a coin and a die and toss them both. What is the probability of getting an even number and a head? a. 1/4 b. 1/2 C. 1/12 d. 8/12 e. 7/12 of anmoton 2. A 3. You have a deck of cards. You choose one card. What is the probability of getting a jack or a club? a. 1/4 b. 13/52 C. 9/12 (d. )16/52 e. 5/52 3. D 4. What is the probability of flipping 5 coins and getting a tail on the first flip and heads on the last 4 flips?=G 1/2 a. 1/4 b. 1/2 C. 1/8 d. 1/16 (e)1/32 4. 5. What is the probability of flipping 5 coins and getting 2 heads and 3 tails in any order? 10/32 b. 1/2 c. 1/8 d. 10/16 e. 1/32 5. A 10*(z) / 10 *32= 10/32 6. Considering four gene loci, what is the probability that an individual with the genotype AaBbCcDd will produce a gamete that has the genotype A B CD ? a. 1/4 b. 1/2 c. 1/8 d. 1/16 e. 1/32 6. D 7. Consider a tetrahybrid cross (AaBbCcDd x AaBbCcDd), what is the probability that offspring will be homozygous dominant for all four traits (AABBCCDD)? a. 1/4 b. 1/16 c. 1/64 d. 1/128 fe. 1/256 7 . E 8. If a tetrahybrid is test crossed (i.e. crossed to a homozygous recessive individual, aabbcodd), what is the probability that a phenotypically recessive individual offspring will be produced? a. 1/4 b. 1/2 c. 1/8 d) 1/16 e. 1/32 8. D 9. In couch potato fleas, pink eyes are dominant to blue eyes and straight wings are dominant to curly. A cross between a homozygous pink eyed, straight wing female is mated with a blue eyed, curly winged male. The F1 progeny are then crossed to produce the F2 generation. What is the probability of producing a blue eyed, curly winged flea in the Fz generation? a. 1/4 b. 1/2 c. 1/8 d.)1/16 e. 1/32 23