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(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!!