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Question 4: Bayes' Theorem involves deriving reasonable guesses at probabilities based on statistics, and then updating those probabilities as you get more information. We will use the statistics below and Bayes' Theorem to derive an initial guess at certain probabilities. Bayes' Theorem states that: Pr(A|B) = Pr(B|A) - Pr(A) Pr(B) In addition to Bayes' Theorem, you might find the Law of Total Probability useful: Pr(A) = Pr(A|B) · Pr(B) + Pr(A|B) · Pr(B). Out of 1000 people total that took COMP2804 last year, 820 passed the final exam.¹. 800 students studied for the final exam. 60 people who did not study still passed the final exam. Use these numbers to define initial probabilities and answer the following questions. a) What is your probability of passing the final exam if you study? b) Prove that Pr(A|B) + Pr(Ã|B) = 1. c) You know someone who failed the final. What is the probability that they studied?

Question 4: Bayes' Theorem involves deriving reasonable guesses at probabilities based on statistics, and then updating those probabilities as you get more information. We will use the statistics below and Bayes' Theorem to derive an initial guess at certain probabilities. Bayes' Theorem states that: Pr(A|B) = Pr(B|A) - Pr(A) Pr(B) In addition to Bayes' Theorem, you might find the Law of Total Probability useful: Pr(A) = Pr(A|B) · Pr(B) + Pr(A|B) · Pr(B). Out of 1000 people total that took COMP2804 last year, 820 passed the final exam.¹. 800 students studied for the final exam. 60 people who did not study still passed the final exam. Use these numbers to define initial probabilities and answer the following questions. a) What is your probability of passing the final exam if you study? b) Prove that Pr(A|B) + Pr(Ã|B) = 1. c) You know someone who failed the final. What is the probability that they studied?

A First Course in Probability (10th Edition)
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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Question 4: Bayes' Theorem involves deriving reasonable guesses at probabilities based on statistics, and then updating those probabilities as you get more information. We will use the statistics below and Bayes' Theorem to derive an initial guess at certain probabilities. Bayes' Theorem states that: Pr(A|B) = Pr(BA) Pr(A) Pr(B) In addition to Bayes' Theorem, you might find the Law of Total Probability useful: Pr(A) = Pr(A|B) - Pr(B) + Pr(AB). Pr(B). Out of 1000 people total that took COMP2804 last year, 820 passed the final exam. ¹. 800 students studied for the final exam. 60 people who did not study still passed the final exam. Use these numbers to define initial probabilities and answer the following questions. a) What is your probability of passing the final exam if you study? b) Prove that Pr(A|B) + Pr(Ã|B) = 1. c) You know someone who failed the final. What is the probability that they studied?
Transcribed Image Text:Question 4: Bayes' Theorem involves deriving reasonable guesses at probabilities based on statistics, and then updating those probabilities as you get more information. We will use the statistics below and Bayes' Theorem to derive an initial guess at certain probabilities. Bayes' Theorem states that: Pr(A|B) = Pr(BA) Pr(A) Pr(B) In addition to Bayes' Theorem, you might find the Law of Total Probability useful: Pr(A) = Pr(A|B) - Pr(B) + Pr(AB). Pr(B). Out of 1000 people total that took COMP2804 last year, 820 passed the final exam. ¹. 800 students studied for the final exam. 60 people who did not study still passed the final exam. Use these numbers to define initial probabilities and answer the following questions. a) What is your probability of passing the final exam if you study? b) Prove that Pr(A|B) + Pr(Ã|B) = 1. c) You know someone who failed the final. What is the probability that they studied?
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