Let A and B be events in a sample space S such that P(A) = 0.33, P(B) = 0.35 and P(A ∩ B) = 0.14. Find P(A | B).
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)
[15] 4. Let E and F be events of sample space S. Let P(E) = 0.3, P(F) = 0.6 and the P(EUF) = 0.7. a) Fill in all probabilities in the Venn diagram shown. S b) Find P(EnF). c) Find P(ENF). d) Find the P(E|F). e) Are E and F independent events? Justify your answer.
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)
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
C3. Let A and B be events associated with sample space S. Using the axioms of probability and possibly the consequences of them to show that P(AUB) P(A) +P(B).
please explain the answer. C3. Let A and B be events associated with sample space S. Using the axioms of probability and possibly the consequences of them to show that P(AUB) P(A) +P(B).
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)
2. Let A and B be events in a sample space such that P(A) -0.5. P(ANB) -0.3 and PLAUB)=0.8. Calculate: 1) P(AB): ii) P(BA): iii) PIBIA B): be independent of A and such that B and Care Let the event C in mutually exclusive. Calculate: iv) P(AC); v) PIANBNC). (8 Marks)
Let A, B, and C be three non-empty events defined on the sample space S, illustrated below. Find an expression for the case where two or more events occur? a. b. c. d.
1. Events A and B are defined on a sample space S such that P((A ∪ B) C) = 0.5 and P(A ∩ B) = 0.2.If P(A) = 0.3, what does P((A ∩ B) | (A ∪ B) C) equal?