6. The prosecutor's fallacy. Let G be the event that some accused person is guilty, and I the eventthat some testimony or evidence presented is in fact true. It has been known for lawyers to argueon the assumption that P(G|T) = P(TIG). Show that this holds if and only if P(G)=P(7).

We have to show that the P(G|T)=P(T|G) iff P(G)=P(T)

Answered: 6. The prosecutor's fallacy. Let G be…

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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Photos and videos have become an important part of the online social experience, with more than half of Internet users posting photos and videos online that they have taken themselves. Let A be the event an Internet user posts photos that he or she has personally taken, and B be the event an Internet user posts videos that he or she has personally taken. Pew Research Center finds that P(A) = 0.52, P(B) = 0.26, and P(A or B) = 0.54. What is the conditional probability that an Internet user posts photos that he or she has personally taken, given that he or she posts videos that he or she has personally taken? (Enter your answer rounded to three decimal places.) Р(A | В) —D
(3.) A system contains components connected in parallel as shown in the diagram. If all components operate inderentently, & each component has probability 0.45 of failing What is the minimum number of components that must be connected in parallel so that th Probability that the system operateds exceeds 0.9999? The minimun number of components that must be connected in parallel is.
b. Determine P(F or D)= P(F or D). (Type an integer or a decimal.) c. Find the probability that a randomly selected adult is male. P(male) = (Type an integer or a decimal.)
7. Given P(A) = 1/3 and P(B) = 1/2 and P(A U B) = 2/3 . . . (d) Find P(BIA) (e) Are events A & B Independent? (f) Are events A & B Mutually exclusive?
Suppose that in a large university, 40% of students work part time, 10% are part of one of the university's sports teams, and 5% both work part time and are part of one of the university's sports teams. Let W be the event that a student works part time, and V be the event that a student is part of one of the university's sports teams. Make sure all your answers are expressed in terms of the events W and V,. 4. А. What is the probability that a randomly selected student works part time or is a part of one of the university's sports teams? В. teams? What proportion of students do not work part time but are part of one of the university's sports С. Are W and V independent events? D. If a student works part time, what is the probability they are also part of one of the university's sports teams? Е. What proportion of students are not part of any of the university's sports teams and work part time?
H6.
where the first outcome is one of X, Y, and Z, and the second outcome in each case is one of A and B. Use the following probabilities instead of those given in your text: Pr[X]=37 Pr[Y]=27Pr[Z]=27Pr[A|X]=45Pr[B|X]=15Pr[A|Y]=23Pr[B|Y]=13Pr[A|Z]=18Pr[B|Z]=78 Pr[(XorY)|B]=
the second photo is an example of resolution

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6. The prosecutor's fallacy. Let G be the event that some accused person is guilty, and 7 the event that some testimony or evidence presented is in fact true. It has been known for lawyers to argue on the assumption that P(G|T)= P(TIG). Show that this holds if and only if P(G)=P(7).