Problem 5. In a tennis game, assume the outcomes of each point are mutually independent.Moreover, Alice wins any given point with probability p while Bob wins any given point withprobability q = 1 - p. Deuce is said to occur if, for the first six points of the game, each ofAlice and Bob has won three points. In order for someone to win the game, either Alice orBob must win the next two points; if neither does, the game returns to deuce. The gamecontinues indefinitely until someone wins two points in a row after any given deuce.Given the game is at deuce, what is the probability the game will end after the nexttwo points?b) Given the game is at deuce, what is the probability Alice eventually wins?

Given information: Probability that Alice wins any given point = p Probability that Bob wins any…

Answered: Problem 5. In a tennis game, assume the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Eye color in humans is determined by a single pair of genes. If both genes are blue-eyed genes, then the person will have blue eyes; if they are both brown-eyed genes, then they will have brown eyes; and if one is a blue-eyed gene and the other is brown-eyed gene, then the person will have brown eyes. A baby receives one gene from each of its parents and the gene it receives is equally likely to be either of the two genes of that parent. Suppose that Mario and both of his parents have brown eyes, but that his sister has blue eyes. (a) What is the probability that Mario possesses a blue-eyed gene? (b) Suppose that Mario’s wife has blue eyes. What is the probability that a child of theirs will have blue eyes? (c) If their first child has brown eyes, what is the probability that their second child will also have brown eyes?
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 0.298
I need help with A, B, C. Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose that P(A beats B) = 0.2P(A beats C) = 0.4P(B beats C) = 0.7 and that the outcomes of the three matches are independent of one another. (a) What is the probability that A wins both her matches and that B beats C? and What is the probability that A wins both her matches? (b) What is the probability that A loses both her matches? (c) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)
Evan is ordering dessert, and he wants the fudge pie. The waitress tells him that he can have up to four toppings: ice cream, chocolate sauce, whipped cream, and a cherry. Since he cannot decide how many of the toppings he wants, he tells the waitress to surprise him. If the waitress randomly chooses which toppings to add, what is the probability that Evan gets just chocolate sauce, and a cherry.
Becky and Carla take an advanced yoga class. Becky can hold 29% of her poses for over a minute, while Carla can hold 35% of her poses for over a minute. Suppose each yoga student is asked to hold 50 poses. Let B the proportion of poses Becky can hold for over a minute and C = the proportion of poses Carla can hold for over a minute. What is the probability that Becky's proportion of poses held for over a minute is greater than Carla's? Find the z-table here. O 0.159 O 0,259 0 0.448 O 0,741 Save and Exit Next Submit Math and rem 96 & 7 8 9. 10
Suppose an oil company is thinking of buying some land for $10,000,000. There is a 60%60% chance of economic growth and a 40%40% chance of recession. The probability of discovering oil is 44%44% when there is economic growth and 32%32% when there is a recession. If there is economic growth and the oil company discovers oil, the value of the land will triple. If they do not discover oil, the value of the land will decrease by 10%.10%. If there is a recession and the company discovers oil, the value of the land will increase by 50%.50%. If they do not discover oil, the land will decrease in value by 75%.75%. What is the expected value of the investment? Give your answer to the nearest dollar. Avoid rounding within calculations. $$ Select the correct interpretation of the expected value. The expected value represents what the actual investment value will be for this land purchase of $10,000,000. The company should make the investment because the expected value…
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Suppose you’re playing Texas Hold ’Em Poker, and you are dealt a hand witha Jack of Clubs and a Queen of Hearts. The river of 5 cards hasn’t been dealtyet, and you’re hoping to get a straight (5 cards with consecutive ranks, such as10,J,Q,K,A or 8,9,10,J,Q). What is the probability that you will get a straightthat uses both the Jack and Queen in your hand? (This last part is to keep theproblem simple, since it’s possible to get a straight that uses neither card in your hand, suchas A,2,3,4,5, all in the river. Besides, in those cases, ALL players would have a straight, sothat’s not so good for you!)Guide: Our goal is to calculate:P(straight using both cards in hand) = # 5-card combinations that get us a straight with the J & Q# 5-card combinations overall .(a) We’ll start with the denominator, which can be done with a singleformula from class: How many 5-card combinations are possible for theriver? (Keep in mind what is in your hand. Note that how many opponents you haveand what…

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