for part (c) , please use part (a)
TOPIC: Set theory and Probability.
for part (c) , please use part (a) 2. Given events A and B (a) let...
2. Given events A and B (a) let C be the event that A will occur and B will not occur. Express C in terms of A and B. Let D be the event that B will occur and A wil not occur. Express D in terms of A and B (b) let E be the event that exactly one of the events A or B will occur. Express E in terms (c) Use the result in (a) to find...
Given events A and B, (a) let C be the event that A will occur and B will not occur. Express C in terms of A and B. Let D be the event that B will occur and A will not occur. Express D in terms of A and B. (b) let E be the event that exactly one of the events A or B will occur. Express E in terms of A and B. (c) Use the result in...
2. Express each of the following events in terms of the events A, B, and C, and the operations of complementation, union, and intersection: (a) at least one of the events A, B,C occurs; (b) at most one of the events A, B, C occurs; (c) none of the events A, B, C occurs; (d) all three events A, B, C occur (e) exactly one of the events A, B, C occurs; (f) events A and B occur, but not...
Problem 3. Show the formula P((An B)U(A n B))- P(A) +P(B)-2P(AnB), which givgs the probability that exactly one of the events A and B will occur. [Compare with the formula P(AU B) P(A) P(B) - P(AnB), which gives the probability that at least one of the events A and B will occur.]
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...
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
Given the following: A, B, and C are events. P[A] = 0.3 P[B] = 0.3 P[C] = 0.55 P[A intersect B] = 0 P[A' intersect B' intersect C'] = 0.1 P[A intersect C'] = 0.2 (i) Write a set expression for each of the following events a through d. (ii) Find the probability of the event. (Please show all work. Use venn diagrams if necessary). (a) At least one of the events A, B, or C occurs. (b) Exactly one...
7. Let A, B, and C be three events. Write out expressions for the following events in terms of A, B, and C, using set notation. (a) A occurs but neither B nor C occurs. (b) A and B occur, but not C (c) A or B occurs, but not C. (d) None of A, B, and C occurs. (e) A, B, or C occurs (n) Exactly one of A, B, and C occurs (g) Exactly two of A, B,...