Answer both Q4, Q5 Question 4: 30% of people caught the flu this year. 80% of people got the flu shot. 20% ofthe people who got the flu shot still caught the flu.¹a) Use the definition of conditional probability and any result we've seen in class to prove:Pr(A) = Pr(A|B) · Pr(B) + Pr(A|B) · Pr(B)b) What is your probability of catching the flu if you did not get the flu shot?c) Use the definition of conditional probability to prove Bayes' Theorem:Pr(A|B) =Pr(B|A) · Pr(A)Pr(B)d) You know someone who caught the flu. What is the probability that they got the flushot?Question 5: You are playing 5 card poker with your friends. In this game you are initiallydealt 5 cards and on each round of betting you can exchange any number of cards to try andget a better hand. You are using a standard deck of 52 cards, and any cards you exchangego into a discard pile and are no longer in play for this hand. All cards are dealt uniformlyat random.In your first hand you are dealt {5◇, 50, 7◊, 8♣, A◊}. You keep the pair of 5's and theace and exchange the 7 and 8 for two more cards. Let C be the event that you receive atleast one more ace, and let D be the event that you receive at least one more 5.a) What is Pr(Cn D)?b) What is Pr(CUD)?c) Are events C and D independent? In other words, is Pr(C^ D) = Pr(C) · Pr(D)?

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Question 4: 30% of people caught the flu this year. 80% of people got the flu shot. 20% of the people who got the flu shot still caught the flu.¹ a) Use the definition of conditional probability and any result we've seen in class to prove: Pr(A) = Pr(A|B) · Pr(B) + Pr(A|B) · Pr(B) . b) What is your probability of catching the flu if you did not get the flu shot? c) Use the definition of conditional probability to prove Bayes' Theorem: Pr(A|B) = Pr(B|A). Pr(A) Pr(B) d) You know someone who caught the flu. What is the probability that they got the flu shot?

Question 4: 30% of people caught the flu this year. 80% of people got the flu shot. 20% of the people who got the flu shot still caught the flu.¹ a) Use the definition of conditional probability and any result we've seen in class to prove: Pr(A) = Pr(A|B) · Pr(B) + Pr(A|B) · Pr(B) . b) What is your probability of catching the flu if you did not get the flu shot? c) Use the definition of conditional probability to prove Bayes' Theorem: Pr(A|B) = Pr(B|A). Pr(A) Pr(B) d) You know someone who caught the flu. What is the probability that they got the flu shot?

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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