7. [-/1 Points] DETAILS HARMATHAP12 7.4.013.MI. MY NOTES ASK YOUR TEACHER Each of urns I and II has 5 red balls, 3 white balls, and 2 green balls. Urn III has 1 red ball, 1 white ball, and 8 green balls. An urn is selected at random and a ball is drawn. If the ball is green, find the probability that urn Ill was selected. (Enter your probabilities as fractions.) (a) Use a probability tree to find the probability. (b) Use Bayes' formula to find the probability. Need Help? Read it Master It 8. [-/1 Points] DETAILS HARMATHAP12 7.4.015. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER There are 3 urns containing coins. Urn I contains 5 gold coins, urn II contains 2 gold coins and 2 silver coins, and urn III contains 3 silver coins. An urn is selected at random and a coin is drawn from the urn. If the selected coin is silver, what is the probability that urn III was selected? (Enter your probabilities as fractions.) (a) Use a probability tree to find the probability. (b) Use Bayes' formula to find the probability. Need Help? Read It 9. [-/1 Points] DETAILS HARMATHAP12 7.4.018. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER What is the probability that a couple will have at least three sons if they plan to have 4 children and if the probability of having a son equals the probability of having a daughter? (Enter your probability as a fraction.) Need Help? Read It 10. [-/1 Points] DETAILS HARMATHAP12 7.4.020. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER In a random survey of students concerning student activities, 30 engineering majors, 27 business majors, 22 science majors, and 17 liberal arts majors were selected. (Enter your probabilities as fractions.) (a) If two students are selected at random, what is the probability of getting two science majors? (b) If two students are selected at random, what is the probability of getting a science major and an engineering major? Need Help? Read It 11. [-/1 Points] DETAILS HARMATHAP12 7.4.022.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The probability that an individual without a college education earns more than $100,000 is 0.2, whereas the probability that a person with a B.S. or higher degree earns more than $100,000 is 0.8. The probability that a person chosen at random has a B.S. degree is 0.2. What is the probability that a person has at least a B.S. degree if it is known that he or she earns more than $100,000? (Round your answer to four decimal places.)12. [-/1 Points] DETAILS HARMATHAP12 7.4.023. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A small town has 7000 adult males and 5000 adult females. A sociologist conducted a survey and found that 60% of the males and 50% of the females drink heavily. An adult is selected at random from the town. (Enter your probabilities as fractions.) (a) What is the probability the person is a male? (b) What is the probability the person drinks heavily? (c) What is the probability the person is a male or drinks heavily? (d) What is the probability the person is a male, if it is known that the person drinks heavily? Need Help? Read It 13. [-/1 Points] DETAILS HARMATHAP12 7.4.501.XP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A survey questioned 1000 people regarding raising the legal drinking age from 18 to 21. Of the 530 who favored raising the age, 370 were female. Of the 470 opposition responses, 140 were female. If a person selected at random from this group is a man, what is the probability that the person favors raising the drinking age? (Enter your probability as a fraction.) Need Help? Read It 14. [-/1 Points] DETAILS HARMATHAP12 7.4.502.XP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A survey questioned 1000 people regarding raising the legal drinking age from 18 to 21. Of the 520 who favored raising the age, 350 were female. Of the 480 who expressed opposition, 190 were female. (Enter your probabilities as fractions.) (a) What is the probability that a person selected at random is a female? (b) What is the probability that a person selected at random favors raising the age if the person is a woman? Need Help? Read It 15. [-/1 Points] DETAILS HARMATHAP12 7.4.029. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER In a Student Activity Participation Study (SAPS) survey, 30 engineering majors, 25 business majors, 20 science majors, 15 liberal arts majors, and 10 human development majors were selected. Seven of the engineering, 10 of the science, 9 of the human development, 6 of the business, and 6 of the liberal arts majors selected for the study were female. (Enter your probabilities as fractions.) (a) What is the probability of selecting a female if one person from this group is selected randomly? (b) What is the probability that a student selected randomly from this group is a science major, given that she is female? Need Help? Read It24. [-/1 Points] DETAILS HARMATHAP11 7.7.029. MY NOTES ASK YOUR TEACHER A man owns an Audi, a Ford, and a VW. He drives every day and never drives the same car two days in a row. These are the probabilities that he drives each of the other cars the next day. Pr(Ford after Audi) = 0.6 Pr(VW after Audi) = 0.4 Pr(Audi after Ford) = 0.8 Pr(VW after Ford) = 0.2 Pr(Audi after VW) = 0.8 Pr(Ford after VW) = 0.2 If he drove the Ford today, what are the probabilities for the cars that he will drive 4 days from today? (Give exact answers. Do not round. Audi Ford VW 25. [-/1 Points] DETAILS HARMATHAP11 7.7.039. MY NOTES ASK YOUR TEACHER For species that reproduce sexually, characteristics are determined by a gene from each parent. Suppose that for a certain trait there are two possible genes available from each parent: a dominant gene D and a recessive gene r. Then the different gene combinations (called genotypes) for the offspring are DD, Dr, rD, and rr, where Dr and rD produce the same trait. Suppose further that these genotypes are the states of a Markov chain with the following transition matrix. Offspring genotype Parent genotype DD Dr DD 0.8 0.2 0 Dr 0.3 0.5 0.2 rr 0 0.7 0.3 Find the steady-state vector for this genotype. (Round your answers to two decimal places.)