Question

for part (c) , please use part (a)

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 a formula for the probability of E in terms of the quantities (d) Compare the resulting formula with the formula for P(F), where F is the event that at of A and B. P(A), P(B) and P(AnB least one of the events A or B will occur

0 0
Add a comment Improve this question Transcribed image text
Answer #1

TOPIC: Set theory and Probability.

Considen the two events A and 8 atins, C The event that A witt oecun and B will not oeeuva Expessed in tenms A and 8 apne, A. ℡ event that and A wite not ecun A and B inEhe events A and 8 one f tha events A and B (A witl oceuvo and B wwilt not deeur on (B will occun ant. A will not ơceuy Expressed n toxms of A and de meed, re 04トart← @ P(c) +P ()P(n2 theo pem clemententare /1 =r@tr@-o - diojoint P(A) -P(anB)AdrUQ/ F = The event that at least one the events A on B reg the additive abi andy we thus get/ ant, p (f)=P(A) tr(e)-r (ANB)

Add a comment
Know the answer?
Add Answer to:
for part (c) , please use part (a) 2. Given events A and B (a) let...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • 2. Given events A and B (a) let C be the event that A will occur...

    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...

    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,...

    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...

    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...

    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...

    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...

    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)...

    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]...

    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...

    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,...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT