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 (BnAc), i.e., verify that any set B can be partitioned using A and Ac. S A= (A-B) U (ANB) P(A) = P(A-B) + P(ANB) PLA-B) = P(A)-P(ANB). B= (B-A) U (ANB) - P(B) = P(B-A) + P(ANB) PCB-A) = P(B)- P(ANB) A B (c) From the result in (b), find a formula for calculating P(BA). A-B AnB B-A A-B, ANB and B-A are disjoi events. So, AUB=(A-B) (AMB) U(B-A) PLAUB)=P(A-B) + P(ANB) + P(B-A] P(AUB) = P(A) + PLB)~P(ANB) (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°
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 (BnAc), i.e., verify that any set B can be partitioned using A and Ac. S A= (A-B) U (ANB) P(A) = P(A-B) + P(ANB) PLA-B) = P(A)-P(ANB). B= (B-A) U (ANB) - P(B) = P(B-A) + P(ANB) PCB-A) = P(B)- P(ANB) A B (c) From the result in (b), find a formula for calculating P(BA). A-B AnB B-A A-B, ANB and B-A are disjoi events. So, AUB=(A-B) (AMB) U(B-A) PLAUB)=P(A-B) + P(ANB) + P(B-A] P(AUB) = P(A) + PLB)~P(ANB) (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°
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)
I already have a solved and need help solving both b and c since they are parts of one single problem, thank you!!
Transcribed Image Text:In this problem you will prove the general disjunction rule.
P(AUB) = P(A) + P(B) - P(An B)
(a) Let A and B be any sets in a field F. Using presence tables, verify that B= (BOA) U (BNA), i.e.,
verify that any set B can be partitioned using A and Ac.
A= (A-B) U (ANB)
• P[A) = P(A-B) + P(A/B)
:: P[A-B)=P(A) -P(ANB)
B= (B-A) U (ANB)
- P(B) = P(B-A) + P(ANB)
P(B-A) = P(B)- P(AMB)
i
A
B
(c) From the result in (b), find a formula for calculating P(BA).
V
B-A
AnB
A-B, AMB and B-A are disjoint
events.
So, AUB=LA-B) (AMB) U(B-A)
PLAUB) = P(A-B) + P(ANB) + P(B-A)
PLAUB)= P(A) + P(B)~P(ANB)
(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'
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