Law of total probabilities
5 Pages

Law of total probabilities

Course: DS 101, Spring 2012

School: CSU Sacramento

Word Count: 788

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Law of total probabilities Archie is taking a course in probability theory. Discussion sessions with the class TA (teaching assistant) conflict with Archie's trips to the beach. Archie has to decide between attending TA sessions, which might help him do better in the probability course, and going to the beach. Archie learns that % of past students who did not attend TA sessions received a grade of B or below in...

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of Law total probabilities Archie is taking a course in probability theory. Discussion sessions with the class TA (teaching assistant) conflict with Archie's trips to the beach. Archie has to decide between attending TA sessions, which might help him do better in the probability course, and going to the beach. Archie learns that % of past students who did not attend TA sessions received a grade of B or below in the course. Archie also learns that % of past students received a grade higher than B. After some thought, Archie decides to attend the TA sessions. Not all of his classmates share his decision; in fact, only out of every of his classmates attend discussion sessions with the TA. Compute the probability that Archie will receive a grade higher than a B in the course. Round your answer to two decimal places. (If necessary, consult a list of formulas.) We'll examine the information in the above paragraph. We'll write for the event "achieves a grade higher than a B." We are told that the probability of this event is . We'll write discussion sessions with the TA," and we'll write We are told that out of every for the event "meets in for the complementary event. students attends discussion sessions with the TA; hence , so that . We are also given information as to the lack of success of students who do not meet with the TA. In particular, we are given that , so . Applied to this scenario, the Law of total probability reads . Filling in all the numerical information, we see that . Solving, we obtain . For additional explanation, see: Essentials of Business Statistics, 3rd Ed. Bowerman et al. Section 4.5: Bayes' Theorem (Optional) Thus, the answer is . Law of total probabilities Archie is stranded in a war zone in the land of the Xhosas. His only chance of survival is to reach Sudland, which lies miles away. There are just two routes to Sudland; one is through a desert, and the other is a long and perilous trek through the mountains. Both routes are terribly dangerous. In the past, % of all who tried to reach Sudland failed. Of all attempts to reach Sudland, out of every were by the desert route. Although it is the longer route, the mountains seem to provide more success: % of those who attempted to reach Sudland through the mountains were successful. To save time, Archie intends to go via the desert. What are his chances making of it through to Sudland? Round your answer to two decimal places. (If necessary, consult a list of formulas.) It is necessary to decode the information given. Let us write for the event "successfully reaches Sudland from Xhosa." We are given that the probability of this event is . There are just two routes: through the mountains or through the desert. Only out of every attempts are made by trekking through the desert; that is, Consequently, . . Given the choice of the mountain route, the probability of reaching Sudland is given as The law of total probability applied to the current situation reads . . Filling in the numerical information, we see that . We deduce that . For additional explanation, see: Essentials of Business Statistics, 3rd Ed. Bowerman et al. Section 4.5: Bayes' Theorem (Optional) Thus, the answer is . Law of total probabilities Archie must travel to a foreign country where a deadly strain of flu has ravaged the population. Already, % of the population has succumbed to the flu and died. There is a vaccine, but because the flu is extremely contagious, it spreads quite rapidly, and to date only out of every people have been vaccinated. Thirty percent of those who are not vaccinated die from the flu. Archie has just enough time to be vaccinated before he leaves. What is the probability that Archie will succumb to the flu and die while he is away? Round your answer to two decimal places. (If necessary, consult a list of formulas.) The inhabitants of the foreign country can be partitioned into two non-overlapping classes, namely those who have been vaccinated and those who have not. We represent the event "has been vaccinated" by the abbreviation , and we represent the event "has not been vaccinated" by the abbreviation are told that the event occurs with probability . The conditional probability that a non-vaccinated person will die from the flu is given as is, . We ; that . We shall also need to use the fact that out of every people have been vaccinated, which we translate as . The law of total probability applied to the current situation reads . Filling in the numerical information, we see that . We deduce that . For additional explanation, see: Essentials of Business Statistics, 3rd Ed. Bowerman et al. Section 4.5: Bayes' Theorem (Optional) Thus, the answer is .

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CSU Sacramento - DS - 101
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Chapter2DescriptiveStatistics:TabularandGraphicalMethodsMcGrawHill/IrwinCopyright2010byTheMcGrawHillCompanies,Inc.Allrightsreserved.2.1GraphicallySummarizingQualitativeData Withqualitativedata,namesidentifythedifferentcategories Thisdatacanbesumm
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Practice Assignment # 10 - Answers1Part A. (Use Connect) 210.6a.x1 151, x2 162,1 6, 2 8,n1 625,n2 625100 36 64 6282 (151 162) 1.96 11 1.96 11 1.96625 625 625 625 10 11 1.96 [11 .784] [11.784, 10.216] 25 Yes; between 10.216 and 11.784 h
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CSU Sacramento - DS - 101
1.value:1 pointsThe card game of Euchre employs a deck that consists of all four of each of the aces, kings, queens, jacks, tens, andnines (one of each suitclubs, diamonds, spades, and hearts). Find the probability that a randomly selected cardfrom a
CSU Sacramento - DS - 101
Practice Assignment #04 - Answers1Part A. (Problems available in Connect) 24.12There are 24 total cards.a.PJ 4124 6b.P(S ) 6124 4c.P J A P J P A P J A 111 0366d.PJ S PJ P S PJ S 11136 4 24 8e.Yes, no; A jack and an ace cannot occur
CSU Sacramento - DS - 101
1.value:1 pointsConsider each of the following probability distributions.Calculate x and x for each distribution.(Round your answers to 4 decimal places.)(a)x01p(x)0.30.7xp(x)01230.250.350.200.20xp(x)20250.10.30.30.3x = x
CSU Sacramento - DS - 101
Practice Assignment #5 - Answers 1Part A. (Use Connect) 25.9a. x = 0(.2) + 1(.8) = .82 x = (0 .8)2(.2) + (1 .8)2(.8) = .16 x = .16 0.4x b. xp( x) 0(. 25) 1(. 45) 2(.2) 3(.1) 1.15all x x 2 (0 1.15) 2 (.25) (1 1.15) 2 (.45) (2 1.15) 2 (.2) (3 1.
CSU Sacramento - DS - 101
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CSU Sacramento - DS - 101
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CSU Sacramento - DS - 101
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CSU Sacramento - DS - 101
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CSU Sacramento - DS - 101
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CSU Sacramento - DS - 101
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