Using the information in part A including the above identity, the union rule, and the product rule, find a formula for P(F) that is similar to the one used in the denominator for the Bayes' Theorem formula.
Using the information in part A including the above identity, the union rule, and the product rule, find a formula for P(F) that is similar to the one used in the denominator for the Bayes' Theorem formula.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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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Using the information in part A including the above identity, the union rule, and the product rule, find a formula for P(F) that is similar to the one used in the denominator for the Bayes' Theorem formula.
Transcribed Image Text:1.) (a) In our proof of Bayes' Theorem, we used the following identity: F = (EF) U (E'N F).
This is true for any sets/events E and F. Illustrate this identity using a Venn diagram, and explain.
E
F
"(En
F) is the part of set F that is also part of set E.
"(E' F) is the part of set F that is not part of set E.
Putting these two parts together by taking their union gives us
set F.
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