Homework Answers
a)
A U (A n B)' =A U (A' U B') =(A u A' u B') =S u B' =S (As A u A' =S cause a event and its complement are mutually exclusive and collectively exhaustive)
b)
(A u (A n B))' =((A u A) n (A u B))' =(A n (A n B))' =(A)' =A'
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5. Given events A and B in the sample space S, simplify the following sets. You...
1. Let A, B and C be events in the sample space S. Use Venn Diagrams...
1. Let A, B and C be events in the sample space S. Use Venn Diagrams to shade the areas representing the following events (32 points) a. AU (ANB) b. (ANB) U ( AB) C. AU ( ANB) d. (AUB) N (AUC)
5. In a given sample space, there are events A and B with P(A) .5, P(B)4,...
5. In a given sample space, there are events A and B with P(A) .5, P(B)4, and P(AnB) (a) What is P(AU B)? (b) What is P(A'nB')? 6. In a given sample space, there are events C and D with P(C) .5 and P(D)-8. Given this information: (a) what is the largest value that PCnDcould possibly be? (b) what is the smallest value that P(Cn D) could possibly be? (hint: use Venn diagrams.) . A bowl contains 4 slips of...
(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},...
(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.
As shown in the Venn diagram below, B and Care events in the sample space S....
As shown in the Venn diagram below, B and Care events in the sample space S. Indicate the event B by shading the appropriate region(s). (If necessary, consult a list of formulas.) S + B x 5 ?
Let A, B and C be three events defined on a sample space S (for the...
Let A, B and C be three events defined on a sample space S (for the purposes of illustration assume they are not disjoint as shown on the Venn diagram below). Find expressions and draw the Venn diagram for the event, so that amongst A, B and C: a. only A occurs b. both A and B occur, but not C c. all three events occur d. none of the events occurs e. exactly one of the events occurs f....
Problem 1.1 Let A, B, C be three events in a sample space S. Each of...
Problem 1.1 Let A, B, C be three events in a sample space S. Each of the statements belovw describes an event built from events A, B, and C. For each statement, express the resulting event in terms of the events A, B, and C using only the complement, union, and intersection operations. Also, for cach statement, draw an appropriate Venn diagram and shade the resulting event. (There may be several ways to write the same statement, you only need...
Problem 1.1 Let A, B, C be three events in a sample space S. Each of...
Problem 1.1 Let A, B, C be three events in a sample space S. Each of the statements below describes an event built from events A, B, and C. For each statement, express the resulting event in terms of the events A, B, and C using only the complement, union, and intersection operations. Also, for each statement, draw an appropriate Venn diagram and shade the resulting event. (There may be several ways to write the same statement, you only need...
5. (a) Write out the set P({a, 2,0}). (b) For sets A, B and C, draw...
5. (a) Write out the set P({a, 2,0}). (b) For sets A, B and C, draw the Venn diagram representing AU( B C), (c) For sets A, B and C, draw the Venn diagram representing (AUD) n(B\C). (d) If A and B are two boxes (possibly with things inside), describe the following in terms of boxes A B, P(A), and A.
2. Given the sample space: Ω = {a,b,c,d) and events: A-(a, b, c} and B {b,...
2. Given the sample space: Ω = {a,b,c,d) and events: A-(a, b, c} and B {b, c, d} Calculate and compare both sides of De Morgan's Laws:
05 (24 marks) Let A, B, and C be three events in the sample space S....
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)
1. Let A, B and C be events in the sample space S. Use Venn Diagrams to shade the areas representing the following events (32 points) a. AU (ANB) b. (ANB) U ( AB) C. AU ( ANB) d. (AUB) N (AUC)
5. In a given sample space, there are events A and B with P(A) .5, P(B)4, and P(AnB) (a) What is P(AU B)? (b) What is P(A'nB')? 6. In a given sample space, there are events C and D with P(C) .5 and P(D)-8. Given this information: (a) what is the largest value that PCnDcould possibly be? (b) what is the smallest value that P(Cn D) could possibly be? (hint: use Venn diagrams.) . A bowl contains 4 slips of...
(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.
As shown in the Venn diagram below, B and Care events in the sample space S. Indicate the event B by shading the appropriate region(s). (If necessary, consult a list of formulas.) S + B x 5 ?
Let A, B and C be three events defined on a sample space S (for the purposes of illustration assume they are not disjoint as shown on the Venn diagram below). Find expressions and draw the Venn diagram for the event, so that amongst A, B and C: a. only A occurs b. both A and B occur, but not C c. all three events occur d. none of the events occurs e. exactly one of the events occurs f....
Problem 1.1 Let A, B, C be three events in a sample space S. Each of the statements belovw describes an event built from events A, B, and C. For each statement, express the resulting event in terms of the events A, B, and C using only the complement, union, and intersection operations. Also, for cach statement, draw an appropriate Venn diagram and shade the resulting event. (There may be several ways to write the same statement, you only need...
Problem 1.1 Let A, B, C be three events in a sample space S. Each of the statements below describes an event built from events A, B, and C. For each statement, express the resulting event in terms of the events A, B, and C using only the complement, union, and intersection operations. Also, for each statement, draw an appropriate Venn diagram and shade the resulting event. (There may be several ways to write the same statement, you only need...
5. (a) Write out the set P({a, 2,0}). (b) For sets A, B and C, draw the Venn diagram representing AU( B C), (c) For sets A, B and C, draw the Venn diagram representing (AUD) n(B\C). (d) If A and B are two boxes (possibly with things inside), describe the following in terms of boxes A B, P(A), and A.
2. Given the sample space: Ω = {a,b,c,d) and events: A-(a, b, c} and B {b, c, d} Calculate and compare both sides of De Morgan's Laws:
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)
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