5) If you were the attacker, and knew that your opponent was trying to maximize their probability of of successfullypreventing your attack, how should you choose {4:} to maximize your probability of a successful attack?(Assume that your strategy is going to leak to your opponent.)6) If you were the attacker, and knew that your opponent was trying to minimize the expected cost of your attack,how should you choose {q} to maximize the expected cost of an attack? (Assume that your strategy is goingto leak to your opponent.)7) If both attacker and defender are trying to maximize and minimize (respectively) the probability of a successfulattack, what strategies are they going to end up following:8) If both attacker and defender are trying to maximize and minimize (respectively) the expected cost of an attack,what strategies are they going to end up following? There are N sites that need protection (number them 1 to N). Someone is going to pick one of them to attack, andyou must pick one to protect. Suppose that the attacker is going to attack site i with probability qi. You plan onselecting a site to protect, with probability p, of selecting site i. The choice of {4;} and {p:} represent the attacker'sand defender's strategy, respectively.

Given that the attacker is going to attack site i with probability qiqi and selecting a site to…

Answered: 5) If you were the attacker, and knew…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose a person is thinking about entering a MarioKart competition at theirlocal videogame store. The competition costs 20 dollars to enter. The competition consists of 10 matches. The person knows that their chance of winning each match is 65% and that each match is independent of the others. The payout for the competition is: WIN ALL 10 Matches: 500 Dollar Prize WIN 9 Matches: 250 Dollar PrizeWIN 8 Matches: 50 Dollar Prize OTHERWISE: Nothing 1) Suppose that this person enters the competition 5 times.What is the probability they break even?(Hint: To break even they would need to win the $50 prize twice and lose the other three times. Use a modified binomial to calculate this probability.)
There are X-Mart and Y-Mart convenience stores. It is assumed that each customer purchases once a week at one of the two supermarkets (but not both). In a study, a sample of 100 buyers was taken for 10 weeks. From this research it is known that if buyers go to X-mart store one week, 85 people will still buy at X-mart store the following week and if buyers go to Y-mart store one week, 70 people will still buy at Y-mart store. mart the following week. 1. Make a table and matrix of transition probabilities. 2. If John purchases at X-mart in the first week, what is the probability that Bob purchases at X-store in the third and fourth weeks?
Suppose you are deciding whether or not to bring an umbrella to school and the weathercan be either sunny or rainy. Initially, you think the probability that it will be sunny isP (S) = 0.6, and the probability that it will be rainy is P (R) = 0.4. If you bring an umbrellaand it rains, your payoff is 6. If you bring an umbrella and it is sunny, your payoff is 9. Ifyou don’t bring an umbrella and it rains, your payoff is 0. If you don’t bring an umbrellaand it is sunny, your payoff is 10. Suppose that you check two websites for weather forecasts.You know that the two forecasts are independent of each other, and each forecast is correct70% of the time. That is, the probability that the website says it will be sunny given that itactually will be sunny is 0.7, and the probability that the website says it will rain given thatit actually will rain is 0.7. Suppose that you suffer from confirmation bias. You initially thinkit is more likely to be sunny, so you misinterpret rain forecasts as sun…
A medical researcher claims that the proportion of patients receiving 200 mg of a newly-developed influenza vaccine who go on to contract influenza strain X is less than the proportion of patients receiving 200 mg of last year's influenza vaccine who contract influenza strain X. Of 320 patients who are given last year's vaccine, 114 contract influenza strain X. Of 350 patients who are given the new vaccine, 112 of them contract influenza strain X. Let PN be the proportion of patients receiving the newly-developed vaccine and pL be the proportion of patients receiving last year's vaccine. State the null and alternative hypotheses and the value of the test statistic. Ho: PN =PL versus HA: PN > PL; Test statistic: Z = 0.99 Ho: PN=PL versus HA: PN > PL; Test statistic: Z = 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 0.99
2. If P(X € A) — .3, P(X € В) %3 .25, Р(X € С) %3 .6, P(Х € AUB) 3 55, аnd P(X € BUС) %3 .7, determine the following probabilities. (а) Р(Х € А') (b) Р(X € В°) (с) Р(X € AnВ) (d) P(Х € ВПС)
The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.45, the analogous probability for the second signal is 0.5, and the probability that he must stop at at least one of the two signals is 0.9. (a) What is the probability that he must stop at both signals? X (b) What is the probability that he must stop at the first signal but not at the second one? X (c) What is the probability that he must stop at exactly one signal?
Suppose that one variable, xx, is chosen randomly and uniformly from [0, 1], and another variable, yy, is also chosen randomly and uniformly from [0, 2]. What is the probability that x≤y≤2x+1x≤y≤2x+1?The probability for x≤y≤2x+1x≤y≤2x+1 is?
Consider the following scenario: • Let P(C) = 0.3• Let P(D) = 0.8• Let P(C|D) = 0.3 A. P(C AND D) = [ Select ] ["0.30", "0.24", "0.26", "0.11"] B. Are C and D Mutually Exclusive? [ Select ] ["No, they are not Mutually Exclusive.", "Yes, they are Mutually Exclusive."] C. Are C and D independent events?[ Select ]["No, they are Dependent.", "Yes, they are Independent."] D. P(C OR D) = [ Select ] ["0.92", "0.86", "0.60", "1.1"] E. P(D|C) = [ Select ]["0.30", "0.95", "0.24", "0.80"]
H6.
Suppose that a magazinemagazine predicted that Candidate A would defeat Candidate B in a certain election. They conducted a poll of its subscribersits subscribers with a response rate of 2424%. On the basis of the results, the magazinemagazine predicted that Candidate A would win with 57% of the popular vote. However, Candidate B won the election with about 62% of the popular vote. At the time of this poll, most subscribers to the magazinesubscribers to the magazine belonged to the party of Candidate A. Name two biases that led to this incorrect prediction.Choose the correct answer below. A.Nonresponse bias: The low response rate caused bias.Response bias: The way the poll was administered showed bias. B.Sampling bias: Using an incorrect frame led to undercoverage.Nonresponse bias: The low response rate caused bias. C.Sampling bias: Using an incorrect frame led to undercoverage.Response bias: The way the poll was administered showed bias. Click to select your answer.
Consider the following game in a game arcade. The probability of winning a game is p and hence loosingthe game is 1 − p. In order to win a prize you are given three choices:• A: win at least once in 6 games;• B: win at least twice in 12 games; and• C: win at least 3 times in 18 games.1. If p = 16 which of A, B, or C should you choose to maximize your probability of winning the prize?You are required to compute the probabilities for each option to justify your answer.2. Using the formulas derived in part (1), write a R-code to compute (not simulate) and plot the probabilityof winning the prize for options A, B, and C for different values of p varying from 0.1 to 0.9 inincrements of 0.1. Summarize your observation.Regarding the plot: i) All three curves should be drawn in the same plot, ii) Make sure that the threecurves are distinguishable (using different line styles, colors, and/or markers), and iii) make sure toadd a legend that identifies the curves for the three different options…

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5) If you were the attacker, and knew that your opponent was trying to maximize their probability of of successfully preventing your attack, how should you choose {q.} to maximize your probability of a successful attack? (Assume that your strategy is going to leak to your opponent.)