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In this problem you will prove the general disjunction rule. P(AU B) = P(A) + P(B) - P(An B)

In this problem you will prove the general disjunction rule. P(AU B) = P(A) + P(B) - P(An B)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In this problem you will prove the general disjunction rule. P(AU B) = P(A) + P(B) - P(An B)
In this problem you will prove the general disjunction rule. P(AUB) = P(A) + P(B) - P(ANB) (a) Let A and B be any sets in a field F. Using presence tables, verify that B = (BNA) U (BNA), i.e., verify that any set B can be partitioned using A and Ac. (b) From (a), derive the formula for calculating P(B) using the rules of probability theory already established in lecture. Make sure to cite the rule you are using. You cannot use Rule 7! (c) From the result in (b), find a formula for calculating P(Bn Ac).
Transcribed Image Text:In this problem you will prove the general disjunction rule. P(AUB) = P(A) + P(B) - P(ANB) (a) Let A and B be any sets in a field F. Using presence tables, verify that B = (BNA) U (BNA), i.e., verify that any set B can be partitioned using A and Ac. (b) From (a), derive the formula for calculating P(B) using the rules of probability theory already established in lecture. Make sure to cite the rule you are using. You cannot use Rule 7! (c) From the result in (b), find a formula for calculating P(Bn Ac).
(d) Using presence tables verify that AUB=AU (BNA). (e) Using the results from (c) and (d) and any other rules of probability theory already established in lecture, derive the formula for the general disjunction rule.
Transcribed Image Text:(d) Using presence tables verify that AUB=AU (BNA). (e) Using the results from (c) and (d) and any other rules of probability theory already established in lecture, derive the formula for the general disjunction rule.
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