5. In a given sample space, there are events A and B with P(A) .5, P(B)4,...
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)
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)
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).
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
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)
Consider the sample space ș = {x | 0 < x < 12), and the events A = {지 2 Find the events: (a) A UB (b) AnB (c) A' n B', and (d) A' UB' x < 5} and B = {지 3 < x < 7}
Refer to the Venn diagram to the right for events A and S B in an equally likely sample space S. Find the indicated probability А B P((ANB)) 40 15 25 20 P((ANB)') = (Type a decimal.)
2. a) Let A and B be two events such that P(A) 4, P(B) .5 and P(AnB) 3 Find P(AUB). b) Let A and B be two events such that P(A)-5, P(B) 3 and P(AUB) .6. Find P(An B)
Problem 1.2 Consider an experiment with sample space S = {1,2,3,4}. Define events A, B, C as A = {1,2}, B = {2,3}, C = {1,4}. (a) Are A, B, C mutually disjoint? Are A, B, C collectively exhaustive? (b) Is it possible to have P[A] + P[B] + P[C] = 1? Explain why or why not. (c) If P[A] + P[B] + PIC] = 1, what is the value of P[A]?