Following is the expressions in set notation corresponding to each of the following events : -------------
a) the event which occurs if exactly one of the events A and B occurs is
(A ∩ Bc ) ∪ (A c ∩ B)
b) the event which occurs if none of the events A, B, or C occurs;
(A c ∩ B c ∩ C c)
Write down the expression in set notation corresponding to each of the following events. a) the...
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...
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,...
1. Suppose that A, B, and C are events such that P[A]- PB0.3, PC 0.55, PIANB]- For each of the events given below in parts (a)-(d), do the following: (i) Write a set expression for the event. (Note that there are multiple ways to write this in many cases.) (ii) Evaluate the probability of the event. Hint: Draw the Venn Diagram. You may then want to identify the probabilities of each of the disjoint regions in the diagram before starting...
1. Suppose that A. B. and C are events such that PA-PlB) = 0.3. PC] = 0.55, PAT B) = For each of the events given below in parts (a)-(d), do the following: (i) Write a set expression for the event. (Note that there are multiple ways to write this in many cases.) (ii) Evaluate the probability of the event. Hint: Draw the Venn Diagram. You may then want to identify the probabilities of each of the disjoint regions in...
1. Suppose that A, B, and C are events such that PIAPB0.3, PC 0.55, PIANB- 0, PAnBn 0.1, and P[An 0.2. For each of the events given below in parts (a)-(d), do the following: (i) Write a set expression for the event. (Note that there are multiple ways to write this in many cases.) (ii) Evaluate the probability of the event. Hin: Draw the Venn Diagram. You may then want to identify the probabilities of each of the disjoint regions...
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. 0-inni-mn u (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.
2. Let A and B be events. Find an expression for the event"exactly one of the events A and B', occurs; simplify your result as far as you can. Draw a Venn diagram for this event.
find the set notation for the following regular expression: L(aa*(ab+a)*). build its corresponding automaton. find a regular grammar for it.
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