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The events A, B and C form a partition of the sample space 2. Suppose that...
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. (10 marks) (a) Let m events Bi, , Bm form a partition of the sample space Ω and let event A be...
1. (10 marks) (a) Let m events Bi, , Bm form a partition of the sample space Ω and let event A be any event such that A c S2. Then show that given Bi > 0 for j = 1,.. ., m (b) Considcr a clinical trial where group of paticnts arc trcated for depression. As in many such trials a patient has two possible out- comes, in this study a relapse and no relapse. Refer to a relapse...
Suppose that Upper A 1A1 and Upper A 2A2 form a partition of the sample space...
Suppose that Upper A 1A1 and Upper A 2A2 form a partition of the sample space S with Upper P left parenthesis Upper A 1 right parenthesis equals 0.75PA1=0.75 and Upper P left parenthesis Upper A 2 right parenthesis equals 0.25PA2=0.25. If E is an event that is a subset of S and Upper P left parenthesis Upper E vertical line Upper A 1 right parenthesis equals 0.06PE A1=0.06 and Upper P left parenthesis Upper E vertical line Upper A...
3. Suppose that A and B are two events defined over the same sample space, with...
3. Suppose that A and B are two events defined over the same sample space, with probabilities P(A) 3/4 and P(B)- 3/8. (a) Show that P(A UB) 2 3/4. (b) Show that 1/8 < P(AB) 3/8 (c) Give inequalities analogous to (a) and (b) for P(A) 2/3 and P(B)1/2.
Exercise 4-5 Algo A sample space, S, yields four simple events, A, B, C, and D,...
Exercise 4-5 Algo A sample space, S, yields four simple events, A, B, C, and D, such that P(A) = 0.19, P(B) = 0.03, and P(C) 0.31 a. Find P(D). (Do not round intermediate calculations. Round your answer to 2 decimal places.) P(D) 0.20 b. Find P(C). (Round your answer to 2 decimal places.) c. Find P(A U B). (Round your answer to 2 decimal places.) P(A U B) References eBook & Resources Worksheet Difficulty: 2 Medium Learning Objective: 04-03...
Exercise 4-5 Algo A sample space, S, yields four simple events, A, B, C, and D,...
Exercise 4-5 Algo A sample space, S, yields four simple events, A, B, C, and D, such that P(A) = 0.25, P(B) = 0.06, and P(C) -0.14 a. Find P(D). (Do not round intermediate calculations. Round your answer to 2 decimal places.) P(D) b. Find P(C.(Round your answer to 2 decimal places.) P(C) c. Find P(A U B). (Round your answer to 2 decimal places.) P(A UB)
In a sample space, events A and B are independent, events B and C are mutually...
In a sample space, events A and B are independent, events B and C are mutually exclusive, and A and C are independent. a) Show that P(AUB) = P(B) + P(A)P(B') = P(A) + P(A')P(B) b) If P(AUBUC) = 0.9, P(B) = 0.5 and P(C) = 0.3 find P(A).
Suppose A and B are events in a sample space Ω. Let P(A) = 0.4, P(B)...
Suppose A and B are events in a sample space Ω. Let P(A) = 0.4, P(B) = 0.5 and P(A∩B) = 0.3. Express each of the following events in set notation and find the probability of each event: a) A or B occurs b) A occurs but B does not occur c) At most one of these events occurs
5. Consider an experiment with sample space S and events A,B,C, and D with the following...
5. Consider an experiment with sample space S and events A,B,C, and D with the following probabil ities: P(AUB)-|, P(A) = P(čnD) = , P(C) = 훙 Furthermore, A and B are mutually exclusive (ie. A กั-o), while C and D are independent (ie. P(cr D) = P(C)P(D)). (Note: I know this looks like a lot of parts, but these are all short, quick answers!) (a) Find P(An (b) Find P(B) (c) Find P(AnB) (d) Find P(AUB) (e) Are A...
Let and B be events in a sample space S, and let C = S -...
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)
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. (10 marks) (a) Let m events Bi, , Bm form a partition of the sample space Ω and let event A be any event such that A c S2. Then show that given Bi > 0 for j = 1,.. ., m (b) Considcr a clinical trial where group of paticnts arc trcated for depression. As in many such trials a patient has two possible out- comes, in this study a relapse and no relapse. Refer to a relapse...
3. Suppose that A and B are two events defined over the same sample space, with probabilities P(A) 3/4 and P(B)- 3/8. (a) Show that P(A UB) 2 3/4. (b) Show that 1/8 < P(AB) 3/8 (c) Give inequalities analogous to (a) and (b) for P(A) 2/3 and P(B)1/2.
Exercise 4-5 Algo A sample space, S, yields four simple events, A, B, C, and D, such that P(A) = 0.19, P(B) = 0.03, and P(C) 0.31 a. Find P(D). (Do not round intermediate calculations. Round your answer to 2 decimal places.) P(D) 0.20 b. Find P(C). (Round your answer to 2 decimal places.) c. Find P(A U B). (Round your answer to 2 decimal places.) P(A U B) References eBook & Resources Worksheet Difficulty: 2 Medium Learning Objective: 04-03...
Exercise 4-5 Algo A sample space, S, yields four simple events, A, B, C, and D, such that P(A) = 0.25, P(B) = 0.06, and P(C) -0.14 a. Find P(D). (Do not round intermediate calculations. Round your answer to 2 decimal places.) P(D) b. Find P(C.(Round your answer to 2 decimal places.) P(C) c. Find P(A U B). (Round your answer to 2 decimal places.) P(A UB)
5. Consider an experiment with sample space S and events A,B,C, and D with the following probabil ities: P(AUB)-|, P(A) = P(čnD) = , P(C) = 훙 Furthermore, A and B are mutually exclusive (ie. A กั-o), while C and D are independent (ie. P(cr D) = P(C)P(D)). (Note: I know this looks like a lot of parts, but these are all short, quick answers!) (a) Find P(An (b) Find P(B) (c) Find P(AnB) (d) Find P(AUB) (e) Are A...
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)
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