1. Let A, B and C be events in the sample space S. Use Venn Diagrams...
05 (24 marks) Let A, B, and C be three events in the sample space S. Suppose we know that A U B U C-S, P(A)-1/2, P(B)-1/3, PALJ B-3/4. Answer the following questions: a) Find P(AnB). (4 marks) b) Do A, B, and C form a partition of S? Why? (4 marks) c) Find P(C-(AUB)). (8 marks) d) If P(Cn (AU B))-5/12, find P(C). (8 marks)
Please help me prove 2,4, and 5. Thank you Theorem 17. Let A, B and C be sets. Then the following statements are true: (1) AB CA; (2) B CAUB; (3) A CAUB; (4) AB=BA; (5) AU (AUC) = (AUB) UC; (6) An(BNC) = (ANB) nC; (7) An (BUC) = (ANB) U (ANC); (8) AU (BAC) = (AUB) n(AUC).
Let and B be events in a sample space S, and let C = S - (AUB). Suppose P(A) = 0.8, P(B) = 0.2, and P(An B) = 0.1. Find each of the following. (a) P(AUB) (b) P(C) (c) PAS (d) PLAC BC) (e) PLACUBS (1) P(BCnc)
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)
Use Venn diagrams to prove or disprove the following c) AU B (An B) u (A n B)u (A n B) d) A U (B n C) (AU B) n (AU C)
5. Given events A and B in the sample space S, simplify the following sets. You can carry out the calculations using the laws of set operations. Alternatively, you can use Venn diagrams to find the answers. a. AU(An B) b. (AU(An B))'
A,C,G please 1. Let A, B, and C be subsets of some universal set u. Prove the following statements from Theorem 4.2.6 (a) AUA=/1 and AnA=A. (b) AUO- A and An. (c) AnB C A and ACAUB (d) AU(BUC)= (A U B) U C and An(B n C)-(A n B) n C. (e) AUB=BUA and A n B = B n A. (f) AU(BnC) (AU B) n(AUC) (g) (A U B) = A n B (h) AUA=1( and An-=0. hore...
(2.3 Review of Set Theory and Venn Diagram) 2.3 If the sample space S={1,2,3,4,5,6} and A={1,2}, B={2,3,5}, C={1,4,6} Find the following sets: a) AU B. b) An C. c) AUB d) Check the distributive law by finding (AU B) C=AN C)U (BNC). e) Check the DeMorgan's law by finding A UC = Ā nē.
-/11.11 points s may Noves not your rescher v Let A and B be two events in a sample space for which Pr(A) - 2/3, Pr(B) - 1/6 and Pr[AnB) - 1/9 a. What is Pr(AUB)? b. What is Pr(AB)? c. What is Pr(BIA)? d. What is Pr )? e. What is Pr(A)? f. What is Pr(B)? 9. What is Pr(CAU B)')?
3. (12') Using Venn diagrams, verify the following identities. (a) A-(AnB)U(A-B) ( b) If A and B are finite sets, we have (AUB)- A+B-(AnB )