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- Baseball's World Series is a maximum of seven games, with the winner being the first team to win four games. Assume that the Atlanta Braves are playing the Minnesota Twins in the World Series and that the first two games are to be played in Atlanta, the next three games at the Twins' ballpark, and the last two games, if necessary, back in Atlanta. Taking into account the projected starting pitchers for each game and the home field advantage, the probabilities of Atlanta winning each game are as follows: Game 1 2 3 4 5 6 7 Probability of Win 0.45 0.42 0.46 0.5 0.46 0.41 0.52 Set up a spreadsheet simulation model in whether Atlanta wins each game is a random variable. What is the probability that the Atlanta Braves win the World Series? If required, round your answer to two decimal places.fill in the blank 1 What is the average number of games played regardless of winner? If required, round your answer to one decimal place.Your group can choose to play one of two games. Each game cost one dollar to play.Game one: a will with three numbers on it-zero, one and two-is spun so that there is 20% chance that the wheel lands on zero a 50% chance of the wheel lands on one and a 30% chance the wheel lands on two. You get back the amount in dollars of the numbers that the real land on what is the expected amount of money you will get back from game one?An auto insurance company classifies each motorist as "high risk" if the motorist has had at least one moving violation during the past calendar year and "low risk" if the motorist has had no violations during the past calendar year. According to the company's data, a high-risk motorist has a 50% chance of remaining in the high-risk category the next year and a 50% chance of moving to the low-risk category. A low-risk motorist has a 90% chance of moving to the high-risk category the next year and a 10% chance of remaining in the low-risk category. In the long term, what percentage of motorists fall in each category? (Round your answers to two decimal places.) high-risk category % low-risk category %
- I need help with thisIn small town there are three different types of whether conditions: sunny day, rainy day, and windy day. A sunny day never happens two days in a row. If it is a sunny day, it is as likely to have a rainy day or windy day the next day. If it is a windy day or rainy day, it has an even chance of having the same conditions next day. For the other 50%, it is two times more likely to have a bad weather conditions than a sunny day. a) (Calculate without using matrix multiplication, hint: calculate just the needed value or matrix element)? b) What is the probability of having sunny 4 days from now, if today is a rainy day? c) What is the probability of having a rainy day 3 days from now if today is a windy day? d) Obtain the mean first passage time for all statesOn a given weekend in the fall, a tire company can buy television and advertising time for a college football game, a baseball game, or a professional football game. If the company sponsors the college football game, there is a 70% chance of a high rating, a 50% chance if they sponsor a baseball game, and a 50% chance if they sponsor a professional football game. The probabilities of the company sponsoring these various games are 0.4, 0.1, and 0.5, respectively. Suppose the company does get a high rating, find the probability that it sponsored a professional football game.
- At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. The probabilities are displayed in the tree diagram. The professor informs the class that there will be a test next week. What is the probability that a randomly selected student studied for the test if they pass it with a B or higher? 0.20 0.55 0.60 0.80A forensic psychologist conducted a study to examine whether being hypnotized during recall affects how well a witness can remember facts about an event. Eight participants watched a short film of a mock robbery, after which each participant was questioned about what they had seen. The four participants in the experimental group were questioned while they were hypnotized and the researcher recorded their accurate responses. The four participants in the control group (not hypnotized) were questioned and the researcher recorded their accurate responses. Here are the results: Accurate Recalled Responses Hypnotized Group 7 8 7 9 Control Group 9 8 11 7 a.) Do hypnotized witnesses perform differently than witnesses who are not hypnotized? Carry out a t-test for independent means (use the .05 significance level). Use the five steps of hypothesis testing. Label all the steps clearly. Show ALL Work/calculations. b.) Report the statistic in APA format (the statistical sentence). ,A man buys a racehorse for $25,000 and enters it in two races. He plans to sell the horse afterward, hoping to make a profit. If the horse wins both races, its value will jump to $105,000. If it wins one of the races, it will be worth $65,000. If it loses both races, it will be worth only $10,000. The man believes there is a 30% chance that the horse will win the first race and a 35% chance that it will win the second one. Assuming that the two races are independent events, find the man's expected profit.
- In an amusement arcade there is a horse race with horses coloured red, yellow and green. Only one player can play this game at any time and the outcomes of each race are independent of previous races. You can either bet 10p or 20p. If you bet 10p then each horse is equally likely to win. If you bet 20p the corresponding probabilities are 50%, 30% and 20%, respectively. Three times as many people bet 10p as do 20p. Given red wins, what is the probability it had been a 20p bet? 0.333 0.300 0.313 0.298Suppose I flip a fair coin n = 20 times. A psychic tries to predict the outcome before each flip. Three researchers have different ideas about the psychic's ability. There is Sydney, the Skeptic (S), who thinks the psychic's success rate is between 49% and 51%. There is Morgan, the Mark, M, who thinks that the psychic's success rate is 80%. And there is Carter, the Cynic (C), who thinks the psychic's success rate is 10%. Specifically: S+ 0 ~ U(.49, .51) M + 0 = .80 C0 = .10 %3D In all cases, assume the number of successful predictions follows a binomial distribution with success rate 0. Usek for the number of successes and n for the number of trials. Given all that: Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over Morgan. Call that Bayes factor Bc:M Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Morgan over Sydney. Call that Bayes factor BM:S Determine the formula for the Bayes factor (a.k.a., likelihood…Example: Mr. Stoneguy, a wealthy diamond dealer, decides to reward his son by allowing him to select one of two boxes. Each box contains three stones. In one box two of the stones are real diamonds, and the other is a worthless imitation; and in the other box, one is a real diamond, and the other two are worthless imitations. If the son were to choose randomly between the two boxes, his chance of getting two real diamonds is 0.5. Mr. Stoneguy then suggested that he will allow his son to draw one stone from one of the boxes and to examine it to see if it is a real diamond and to decide which box to select. The son agreed and decided to take the box that the stone he tested came from if the tested stone is real and to take the other box otherwise. Will this strategy increase the son's chance of getting two real diamonds? There are 2 stages in this experiment: Stage 1- selection of box at random Stage 2 - selection of stone at random from the selected box in Stage 1 Let A = event of…
