Let A and B be events in the same sample space, such that Pr[A] = 2/5, Pr[B] = 3/10, and Pr[A|B] = 2/3. What is Pr[B|A]?
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Let A and B be events in the same sample space, such that Pr[A] = 2/5,...
independent events A and B in a sample space S, but assume that Pr[A]=0.3 and Pr[B]=0.15. Compute the following conditional probabilities: (1) Pr[A|B]= equation editorEquation Editor (2) Pr[B|A]= equation editorEquation Editor
3. (2 poi ints) Let A and B be independent two events in a sample space. Also, assume that the probability of occurring A is two times of occurrin g B. If P(A n B) 0.2, what are P(A) and P(B)?
F and G are disjoint events in sample space S . If Pr(F)=0.35, and Pr(G)=0.4, find each of the following probabilities. What is Pr(F∩G)? What is Pr(F′∩G′)? What is Pr(G′|F)? What is Pr(G|F)?
Events A and B are defined on the same sample space that has 20 outcomes. A∩B includes 3 outcomes, AC∩B includes 5 outcomes and A∩BC includes 6 outcomes. How many outcomes are in (A∪B)C?
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).
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.
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)
A and B of a sample space S, but assume that Pr[A]=0.2 and Pr[B]=0.6. Find Pr[A∪B] under each of the following conditions: (1) If A⊂B, then Pr[A∪B]= (2) If A∩B=∅, then Pr[A∪B]= (3) If A∩B′=∅, then Pr[A∪B]=
J,K, and L are events in sample space S. Pr(J)=0.3 Pr(K)=0.34 Pr(L)=0.43 Pr(J intersect K)=0.16 Pr(J' intersect L')=0.44 Pr(K' intersect L)=0.24 What is Pr(L|J)? What is Pr(K|L')?
-/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)')?