Show proof of P(AUBUC) - P(A)+P(B) +PCC) - P(ANB) -P(BnC)-Planc) + P(AMBAC) use D to replace...
3. Let A, B, C be events in a sample space S. Prove that (a) P(AUB) P(A)P(B), (b) P(AUBUC) P(A)+P(B)+P(C)-P(AnB)-P(Anc)-P(Bnc)+P(AnBnc)
Exercise 4. By writing AU BUC as (AUB) UC, show that the Principle of Inclusion-Exclusion for three sets is P(AUBUC) = P(A)+P(B)+P(C)- P(ANB) - P(ANC) - P(BNC)+P(ANBNC) Can you generalize the result to an arbitrary number of events?
write the proof problem 3
2. Let A, B and C be sets, then Au(Bnc)-(AUB)n (Auc) 3. Let A and B be sets, then (An B)c-AcUBc.
1 Let A and B be independent events with P(A) and P(B) = FICE Find P(ANB) and P(AUB). 8 P(ANB) = P(AUB) =
3. A committee is formed consisting of four executives, two women (Susan and Mary) and two men (Bill and Peter). A chairperson and a secretary are selected randomly by drawing straws a) List the sample space and the outcomes comprising each of the following events (you can use shorthand notation for names, a table etc.) A fa woman is appointed chairperson, B-Bi is appointed secretary, C Mary is appointed secretary, AUB,AUBUC, AnB, BnC, AUB, AnB'. b) Find the probabilities of...
(5) 3. A committee is formed consisting of four executives, two women (Susan and Mary) and two men (Bill and Peter). A chairperson and a secretary are selected randomly by drawing straws. a) List the sample space and the outcomes comprising each of the following events (you can use shorthand notation for names, a table etc.) A fa woman is appointed chairperson), B- (Bill is appointed secretary), C Mary is appointed secretary), AUB, AUBUC, AnB, Bnc, AUB, AnB' ). b)...
If P(A)=0.7 ,P(B') = 0.6 and P(AUB)=0.9, then P(ANB) = ? 2. If P(A)=0-7, P(B)=0.6 and P(AUB) - 0.9, then plAl(AUB)) = ? 3 Afair dice is rolled, probability of getting a number & such that 1 <x<8 is = ?
8. Let P(A) P(B) - 1/3 and P(AnB) 1/10. Find the following: (b) P(AUB') () P(Bn A (d) PA UB)
By only use these axioms to solves the following two
questions. Thank you.
(AUB)A nB (AnB) AUB 0 EPCA)E P(S)=I PCAUB) P(A) P(B)-PIAne) P(AIB) # ot times A and Boccur #ot times B ocuuts P(ADP(ANB) PCB) P/AB)P(BIA)P(A) P(B) Taew ledr- Using notin The defa P (A I8), The 3 axioms, and T "lews" Teem we have discussed (e. more 1 Show TR P(ALB ) PLACIB) uw-leuti9-2AsSsume AnBUc) (AnB) U (ANC) Mew show Tt Pl(AU B)UC) PIAT+ PCB) Pc) PCANB) PIANC)-...
2) Suppose A and B are independent events, then() is incorrect. PCAIB) P(A) O P(AnB) P(A)P(B) P(AUB)-P(A)+P(B) 0:(AIB) = P(A)