12. Imagine that the proportion of all e-mails in our training data that are spam is .62, and theproportion of e-mails that are ham is .38. An e-mail comes through our Bayesian filter and itcontains only two words: "lucrative lottery." From our training data, we know the probabilities thateach of these words would appear in either type of e-mail. The probabilities are shown below:SPAMНАМlucrative.05.01lottery.15.03Using a naive bayes methodology, what is the probability that this e-mail is spam?

From the given information, the proportion of the emails spam is, P(Spam) = 0.62. The proportion of…

Answered: 12. Imagine that the proportion of all…

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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36. Consider all courtroom trials with a single de- fendant who is charged with a felony. Suppose that you are given the following probabilities for this situation. Seventy-five percent of the defendants are, in fact, guilty. Given that the defendant is guilty, there is a 70 percent chance the jury will con- vict the person. Given that the defendant is not guilty, there is a 40 percent chance the jury will convict the person. For simplicity, assume that the only options available to the jury are: to convict or to release the defendant. (a) What proportion of the defendants will be convicted by the jury? 38 (b) Given that a defendant is convicted, what is the probability the person is, in fact, guilty? (c) What is the probability that the jury will make a correct decision? (d) Given that the jury makes an incorrect de- cision, what is the probability that the de- cision is to release a guilty person?
20. If the B column of your Z Table disappeared, which of the following could be used to determine B column probabilities? (hint: to help yourself, draw these choices) a. D column - .5000 b. C column - .5000 c. 1-D column d. 1-C column
Richard has just been given a 10-question multiple-choice quiz in his psychology class. Each question has five answers, of which only one is correct. Since he has not attended class recently, he doesn’t know any of the answers. What makes up a trial? What is a success? What is a failure? What are the values of n, p, and q? Assuming Richard guesses on all 10 questions, find the indicated probabilities. What is the probability that he will answer all 10 correctly. What is the probability that he will answer all 10 incorrectly. What is the probability that he will answer at least one of the questions correctly. What is the probability that he will get at most 3 correct? What is the average number(expected value) of questions Richard will answer correctly What is the standard deviation?
Refer to the contingency table shown below. Smoking by Race for Males Aged 18 to 24 Smoker(S) Nonsmoker(N) Row Total White(W) 290 560 850 Black(B) 30 120 150 Column Total 320 680 1,000 Click here for the Excel Data File (a) Calculate the probabilities given below (Round your answers to 4 decimal places.): Smoking by Race for Males Age 18-24 Smoker Nonsmoker Row Total (S) (N) White (W) 290 560 850 Black (B) 30 120 150 Column Total 320 680 1000 Smoking by Race for Males Age 18-24 Smoker Nonsmoker Row Total (S) (N) White (W) 290 560 850 Black (B) 30 120 150 Column Total 320 680 1000
In the football game it is quite common that players suffer injuries. THE NFL reported several injuries suffered by players, some of them are minor, moderate and major. The following table presents the reported injuries: What is P(G|A)?
6. A large group of people is to be checked for two common symptoms of a certain disease. It is thought that 20% of the people possess symptom A alone, 30% possess symptom B alone, 10% possess both symptoms, and the remainder have neither symptoms. For one person chosen at random from this group, find these probabilities (a) The person has neither symptom. (b) The person has at least one symptom. (c) The person has both symptoms, given that the person has symptom B.
On Mr. Casper's debate team at Thunderbird High School, 20% of the members are Sophomores, 35% are Juniors and 45% are Seniors. A team member is selected randomly to give the closing argument for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. If a junior gives the closing argument, the probability of winning is 0.6. If a senior closes, the probability of winning is 0.85. (a) Find the probability that the team wins the debate. b sketch a tree diagram to model this process
Week 7 Homework Question Q1. There exists a deck of 15 cards contain 5 red cards, 5 blue card and 5 green cards. The cards are in a random order, and I turn them over, one at a time: Card 1, Card 2, ..., Card 15 without replacement. In this case, evaluate the following probabilities. i. Card 3 is red ii. Card 1 is red and Card 2 is not blue iii. Card 5 is blue or Card 8 is green iv. Card 2 is green given that Card 1 is green v. A colour appears more than once in the first 3 cards
In an inspection of automobiles in a certain Country, 60% of all automobiles had emissions that did not meet EPA regulations. For a random sample of 10 automobiles, compute the following probabilities: a. All 10 automobiles failed the inspection. b. Exactly 6 of the 10 failed the inspection. c. Six or more failed the inspection. d. All 10 passed the inspection.

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