1.where the first outcome is one of A and B the second outcome in each case is one of a and b. Use the following probabilities instead of those given in your text: Pr[A]=4/7 Pr[B]=3/7 Pr[a|A]=1/3 Pr[b|A]=2/3 Pr[a|B]=1/3 Pr[b|B]=2/3 Find the following missing probabilities: (1)Pr[B]= (2)Pr[b]= (3)Pr[b|B]= (4) [B|b]= 2. where the first outcome is one of X and Y the second outcome is one of A and B if the first outcome is X, and one of A, B, and C if the first outcome is Y. Use the following probabilities instead of those given in your text: pr[x]=.8 pr[y]=.2 pr[A/X]=.7 Pr[B/X]=.3 Pr=[A/Y]=.3 Pr=[B/Y]=.4 Pr=[C/Y]=.3 Find the following misiong probabilities: 1) pr[A]= 2) Pr[X|A]= 3) Pr=[Y|B]= 4) Pr=[B|Y]= 3. where the first outcome is one of X, Y, and Z, and the second outcome in each case is one of A and B. Use the following probabilities instead of those given in your text: Pr[X]=3/7 Pr[Y]=2/7 Pr[Z]=2/7 Pr[A|X]=4/5 Pr[B|X]=1/5 Pr[A|Y]=1/3 Pr[B|Y]=2/3 Pr[A|Z]=1/8 Pr[B|Z]=7/8 Find the following missing probabilities: 1) Pr[B|Y]= 2) Pr[Y|B]= 3) Pr[X OR Y|B]= 4.involving the selection of a colored ball from one of three bowls. Assume that you randomly pick one of the bowls: X, Y, or Z. You then randomly draw one ball out of the selected bowl and note its color. The bowls contain the following colored balls: Bowl X: 1 red, 4 white, and 2 blue. Bowl Y: 4 red, 2 white, and 2 blue. Bowl Z: 1 red, 4 white, and 2 blue. (1) If the ball is blue, what is the probability that it was drawn from bowl X? 1/7 (2) If the ball is either blue or white, what is the probability that it was drawn from bowl Y? 5. involving the selection of colored balls from a box. Assume that the box contains 8 balls: 3 red, 1 green, and 4 blue. Two balls are drawn at random, one after the other without replacement. What is the probability that the first ball was blue, given that the second was red 6. involving the drawing of two balls from a box of colored balls. Assume the box contains 10 balls: 4 red, 3 blue, and 3 yellow. A ball is drawn and its color noted. If the ball is yellow, it is replaced; otherwise, it is not. A second ball is then drawn and its color is noted. What is the probability that the first ball was yellow, given that the second was red? 7. , involving the flipping of either a fair or weighted coin. Assume that the weighted coin yields a heads with probability 0.3. You select one of the two coins at random, and flip it 3 times, noting heads or tails with each flip. What is the probability that the weighted coin was selected, given that all 3 flips turned up heads? 8. Assume that the store stocks 40 percent brand A, 40 percent brand B, and the rest are brand X. Assume further that 10 percent of brand A, 20 percent of brand B, and 25 percent of brand X will not provide the number of pages advertised. A customer buys a cartridge at random. If the customer returns the cartridge because it does not provide the number of pages advertised, what is the probability that the cartridge was brand X? 9. . Assume that 55 percent of the students at the university have taken 4 years of high school math. Of those with four years of high school math, 70 percent plan to major in science. Of those without 4 years, only 20 percent plan to major in science. You stop a student at random. If the student plans to major in science, what is the probability that this student had four years of high school math? 10. Assume that 30 percent are of type A, 30 percent of type B, and 40 percent of type C. It is known that 40 percent of seeds of type A, 50 percent of type B, and 60 percent of type C have germinated. A seed is selected at random. If the seed has germinated, what is the probability that it is of type A? 11. Assume that shoes are produced in three countries: 20 percent in Korea, 50 percent in Canada, and 30 percent in Chile. At the plant in each country, two types of shoes are made: racing shoes and training shoes. The production at each plant as allocated as shown in the table below. The shoes are randomly distributed to stores in the United States, and you purchase one pair from one of these stores. Plant Racing Training Korea 0.8 0.2 Canada 0.4 0.6 Chile 0.7 0.3 If you purchase a pair of training shoes selected at random, what is the probability that they were made in Korea? 12. Assume that the class consists of 25 percent freshmen, 25 percent sophomores, 30 percent juniors, and 20 percent seniors. Assume further that 50 percent of the freshmen, 50 percent of the sophomores, 30 percent of the juniors, and 10 percent of the seniors plan to go to medical school. One student is selected at random from the class. (1) What is the probability that the student plans to go to medical school? (2) If the student plans to go to medical school, what is the probability that he is a senior? 13. Assume that the car lot contains 35 percent Corvettes, 20 percent BMWs, and 45 percent Volvos. Of the Corvettes, 50 percent have navigation systems, 20 percent of the BMWs have navigation systems, and 40 percent of the Volvos have navigation systems. You are assigned a car at random. If the car has a navigation system, what is the probability that it is not a Corvette 14. Assume that the car lot contains 35 percent BMWs, 45 percent Jaguars, and 20 percent Volvos. Of the BMWs, 10 percent have navigation systems, 50 percent of the Jaguars have navigation systems, and 60 percent of the Volvos have navigation systems. Furthermore, 70 percent of the BMWs, 90 percent of the Jaguars, and 40 percent of the Volvos are silver. The property of being silver is independent from having a navigation system. You are assigned a car at random. If the car has a navigation system and is silver, what is the probability that it is a BMW 15. Use the following values instead of those found in your book. (1) 3 successes in 5 trials with p = 0.6: (2) 2 successes in 5 trials with p = 0.3: (3) 0 successes in 4 trials with p =1/4 Use the following values instead of those found in your book. (1) 3 successes in 6 trials with q = 0.8 16. (2) 8 failures in 10 trials with q = 0.65 17. If your text about a multiple-choice test in which each question has 4 choices only one of which is correct. Assume that 9 questions are answered by guessing randomly. What is the probability of getting exactly 3 correct answers