11 Bob has glued himself to a certain slot machine for four hours in a row now with his bucket of coins and a bad attitude. He doesn't want to leave because he feels the longer he plays, the better chance he has t win eventually. Is poor Bob right?
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- The bus is late or my watch is fast.Fifty-eight out of 200 students are 12 or 13 years. Half of the rest are older than 13years and the other half are younger than 12 years. What percent of the students are 12 and 13? What percent of the students are older than 13? How many students are younger than 12? the fish market is selling several different kinds of fish. There are no prices listed. You ask about the prices, but the fish seller will only tell you this:• A pound of salmon and a pound of bass are $12.• A pound of bass and a pound of swordfish are $10.• A pound of salmon and a pound of swordfish are $8.• A pound of swordfish and a pound of catfish are $5.How much is each pound of fish? Show your work. (Each price per pound is a whole dollar amount.) A rectangular polygon consists of 8 squares placed side by side. If the perimeter of the rectangle is 180 inches, what is the area of the rectangle in square inches? A well is 24 feet deep and a snail climbs up 4 feet…Suppose you are playing a simple game that costs you $5 per play, where you draw one cardfrom a well-shuffled deck of 52 cards.• If the card is a spade, you receive $20. (You don’t get the $5 back.)• If it is not, then you do not receive any money. (You don’t get the $5 back.)Let X = the amount of money you have before playing a round of this “game”.Let Y = the amount of money you have after playing a round of this “game”.(a) Compute the conditional expectation of Y given X = $100.(b) You can also use the following variant of the Law of Total Expectation tocompute a conditional expectation:E(Z | X = x) = Summation(E(Z | Ai ∩ X = x)P (Ai | X = x)For this part, let Z = the amount of money you have after playing TWO rounds ofthis “game”. Use the above formula to calculate the conditional expectation of Z givenX = $100. (Note: the cards are well-shuffled again between rounds.)(c) Now suppose you get only $16 for drawing a spade. Compute the conditionalexpectation of Y (not Z) given X =…
- 4. On a game show, you start with a prize pool of $1 000 000, but before you get it, you must answer trivia questions. Every time you get a question wrong, the current prize pool is cut in half, and you must keep answering questions. The game ends when you get a question right and you receive whatever is left of the prize pool. (For example, if you get the first two questions wrong, the prize pool is cut in half twice, so it becomes $250 000. If you then get the third question right, you go home with $250 000 as your winnings.) (a) If you have a chance of getting each question right, what is the distribution of Q: the total number of questions you have to answer? (Give the name of the distribution and its parameters.) (b) Express the amount of money you win as a function of Q. (c) Find the expected amount of money you win.Suppose 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…Mark is a university student and currently studying Statistics. He likes this girl, Lucy, and wants to ask her out on a date. He knows that he might be rejected, accepted, or getting a maybe. So he thought of asking her out twice instead of just once, in case he got rejected in the first try. He defines a success as getting at least one acceptance, no matter whether it is in the first or second try (or both if he's lucky!). What is the probability that he's lucky assuming that he's successful? (Round your answer to two decimal places.)
- You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to roll a six-sided die. She will give you $4 times the number that appears on the die. Your mother says she wants you to spin a spinner with two outcomes, blue and red, on it. She will give you $5 if the spinner lands on blue and $15 if the spinner lands on red. Determine the expected value of each game and decide which offer you should take. The expected value for your sister's game: $$ The expected value for your mother's game: $$ Which offer should you take?This game is called “Get Negative”. Roll two dice (record these in the order you roll them), and then do then do the following: take the first number rolled and subtract 2 times the second number rolled. Regardless of who rolls, Player A gets 3 points if the product is greater than or equal to 0 (i.e. it is zero or positive); Otherwise Player B gets 1 points. The players may or may not take turns rolling the dice as it does not matter who is rolling. Any player may score on any roll, and every roll will result in a score. Play the game by rolling the dice 25 times. For each turn, keep a record of both dice and the resulting answer and the points scored, according to the rules above. Tally the points and calculate the final score for each player. Remember, someone gets a point for each turn, depending on the numbers rolled. (One does not have to be rolling to receive the points.) (Note: you may test the game by yourself by doing all of the 25 rolls yourself and just giving the…This game is called “Get Negative”. Roll two dice (record these in the order you roll them), and then do then do the following: take the first number rolled and subtract 2 times the second number rolled. Regardless of who rolls, Player A gets 3 points if the product is greater than or equal to 0 (i.e. it is zero or positive); Otherwise Player B gets 1 points. The players may or may not take turns rolling the dice as it does not matter who is rolling. Any player may score on any roll, and every roll will result in a score. Play the game by rolling the dice 25 times. For each turn, keep a record of both dice and the resulting answer and the points scored, according to the rules above. Tally the points and calculate the final score for each player. Remember, someone gets a point for each turn, depending on the numbers rolled. (One does not have to be rolling to receive the points.) (Note: you may test the game by yourself by doing all of the 25 rolls yourself and just giving the…
- Mike's game consists of selecting two balls, without replacement, from an urn containing 7 balls numbered 1 through 7. The amount that you win (in dollars) is the maximum of the numbers on the two balls. How much should be charged to play this game if the Mike wants to make $0.90, on average, each time the game is played?Alonzo, Bob, and Casper work bussing tables at a restaurant. Alonzo has a 35% chance, Bob has a 40% chance, and Casper has a 25% chance of bussing tables in the middle area of the restaurant. If Alonzo is bussing tables, he has a 5% chance of breaking a dish. If Bob is bussing tables, he has a 2% chance of breaking a dish. Finally, if Casper is bussing tables, he has a 4% chance of breaking a dish. If there is a broken dish in the middle of the restaurant, what is the probability it was broken by Casper?you are playing a game in which a single die is rolled. if a 2 or a 5 comes up, you win $24, otherwise you lose $3. what is the price that you should pay to play game that would make the game fair?
