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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- At roulette, there are 38 slots. A "column" consists of 12 of these slots. A column pays 2 to 1. So, if you risk $1 on a column and win, you net gain +2 dollars. If you lose, your net equals –1 dollar. Suppose you will play for 100 rounds and bet one dollar on a column each round. (You may enter values rounded to the nearest cent. Beware of carried rounding error.) Your average net gain per play equals 0.0526 dollars. The SD of your net gain per play equals 1.39 dollars. The expected value of your total net gain after 100 plays equals -5.3 dollars. The standard error of your total net gain after 100 plays equals 13.94 dollars.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…
- 3.) Nathan plays a video game in which he starts with 0 points. In round 1, he loses 3; points; in round 2, he wins 28- points; and in round 3, he loses another 3 points. What is his final score?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.Sam enrolled in a Calculus course by mistake, and only discov- ered this after the end of classes. He decides to show up to exam anyway. The exam consists of 54 multiple-choice questions, worth 1 mark each with possible answers (a), (b), (c), (d), (e), (f ). He has no clue how to answer any of the questions, so fills in answers guessed at random. (a) What is his mean score? (You must justify your answer to receive credit). (b) What is the variance of his score? (c) What (approximately) is the probability that he gets 15 or more questions correct?
- Dr. Lawrence has minimized his wardrobe during the fall of 2020, since there's no reason to dress up fancy these days. He has three pairs of jeans, five sweatshirts, and four hats that he puts to regular use. If he were to select his outfit for the day at random, how many different jean-sweatshirt-hat combinations are there? 6.As you entered a casino, an oversized gold bowl containing four dice is presented to you. Pick one die, inspect it just to make sure it is the luckiest one, and then place a $100 chip in the bowl. The dealer will pick one from the remaining dice and modestly places a $100 into the bowl. Next, you and the dealer roll the respective dice. Whoever rolls higher number wins the two chips. Simple. To make the game interesting, the four dice are not the regular dice. While each die has six sides as usual, their faces are marked in unusual ways. One die, call it die A, has two 6’s and four 2’s. Another (die B) has three 5’s and three 1’s. The third one (die C) has four 4’s and two blank faces. The last one (die D) has six 3’s. The dice are not weighted that is, any face is as likely to land face up as any other. Since the game has recently been introduced, the Casino would like to promote the game. For a limited time (this an extremely rare event), the Casino allows the player (in this case,…A student in a statistics class is going to select 5 of her classmates to ask a survey question. Of her 19 classmates, there are 8 students who live on campus and 11 students who live off campus. (a) In how many ways can she select 5 classmates if the number of students who live off campus must be greater than 2? (b) In how many ways can she select 5 classmates if the number of students who live off campus must be less than or equal to 2?
- 3. Tamir has recently begun a new job of selling custom bracelets! Tamir's sales have been growing every week and now he is looking to analyze his profit. Specifically, Tamir is looking to find how much his cost of goods is for his business of selling bracelets. Luckily, Tamir sells each bracelet for the same price and has recorded that when he sold 4 bracelets he made a $39 profit, when he sold 9 bracelets he made a $94 profit. a. Write an equation in point slope form that could model this scenario. b. Which of the following could be the graph of Tamir's profit? Explain how you know. Graph 1: Graph 2: + +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 spin a spinner with two outcomes, blue and red, on it. She will give you $10 if the spinner lands on blue and $20 if the spinner lands on red. Your mother wants you to spin a spinner with six outcomes, numbered 1 through 6, on it. She will give you $3 three times the number that the spinner lands on. Determine the expected value of each game and decide which offer you should take. The expected value for your sister's game: $$ Anticipated value for your mother's game: $$ Which offer should you take? Your sister's offer or your mother's offer?Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 60% of their games.To make up for this, if Doug wins a game he will spot Bob five points in their next game. If Doug wins again he will spot Bob ten points the next game, and if he still wins the next game he will spot him fifteen points, and continue to spot him fifteen points as long as he keeps winning. Whenever Bob wins a game he goes back to playing the next game with no advantage.It turns out that with a five-point advantage Bob wins 60% of the time; he wins 70% of the time with a ten-point advantage and 90% of the time with a fifteen-point advantage.Model this situation as a Markov chain using the number of consecutive games won by Doug as the states. There should be four states representing zero, one, two, and three or more consecutive games won by Doug. Find the transition matrix of this system, the steady-state vector for the system, and determine the proportion of games that Doug will win in the…
