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Bayes' Theorem: Suppose that E and F are two events from a sample space S such that p(E) 0 and p(F) #0. Then: Question: P(F\E)= P(EF)P(F) P(E\F)P(F)+P(EF)P(F) We have two boxes. The first box contains two green balls and seven red balls. The second contains four green balls and three red balls. Bob selects one of the boxes at random. Then he selects a ball from that box at random. If he has a red ball, what is the probability that he selected a ball from the first box. Let E be the event that Bob has chosen a red ball and F be the event that Bob has chosen the first box. The questions is: To find P(FIE) by using Bayes' theorem.

Bayes' Theorem: Suppose that E and F are two events from a sample space S such that p(E) 0 and p(F) #0. Then: Question: P(F\E)= P(EF)P(F) P(E\F)P(F)+P(EF)P(F) We have two boxes. The first box contains two green balls and seven red balls. The second contains four green balls and three red balls. Bob selects one of the boxes at random. Then he selects a ball from that box at random. If he has a red ball, what is the probability that he selected a ball from the first box. Let E be the event that Bob has chosen a red ball and F be the event that Bob has chosen the first box. The questions is: To find P(FIE) by using Bayes' theorem.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section: Chapter Questions
Problem 3P: Dividing a Jackpot A game between two pIayers consists of tossing coin. Player A gets a point if the...
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Bayes' Theorem: Suppose that E and F are two events from a sample space S such that p(E)0 and p(F) 0. Then: Question: P(FE)= P(EF)P(F) P(EF)P(F)+P(EF)P(F) We have two boxes. The first box contains two green balls and seven red balls. The second contains four green balls and three red balls. Bob selects one of the boxes at random. Then he selects a ball from that box at random. If he has a red ball, what is the probability that he selected a ball from the first box. Let E be the event that Bob has chosen a red ball and F be the event that Bob has chosen the first box. The questions is: To find P(FIE) by using Bayes' theorem.
Transcribed Image Text:Bayes' Theorem: Suppose that E and F are two events from a sample space S such that p(E)0 and p(F) 0. Then: Question: P(FE)= P(EF)P(F) P(EF)P(F)+P(EF)P(F) We have two boxes. The first box contains two green balls and seven red balls. The second contains four green balls and three red balls. Bob selects one of the boxes at random. Then he selects a ball from that box at random. If he has a red ball, what is the probability that he selected a ball from the first box. Let E be the event that Bob has chosen a red ball and F be the event that Bob has chosen the first box. The questions is: To find P(FIE) by using Bayes' theorem.
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