Question

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:

  1. a) A or B occurs

  2. b) A occurs but B does not occur

  3. c) At most one of these events occurs

0 0
Add a comment Improve this question Transcribed image text
Know the answer?
Add Answer to:
Suppose A and B are events in a sample space Ω. Let P(A) = 0.4, P(B)...
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
  • Let E and F be two events of an experiment with sample space S. Suppose  P(E)= 0.4,...

    Let E and F be two events of an experiment with sample space S. Suppose  P(E)= 0.4, P(F)=0.3, P(E  U F) =0.5,  Find  P(F|E)   and determine if the two events are independent. A) P(F|E)= 3/4, E and F are independent. B) P(F|E)= 3/4, E and F are not independent. C) P(F|E)=1/2 , E and F are independent. D) P(F|E)= 1/2, E and F are not independent.

  • 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....

  • 2. Let A and B be events in a sample space such that P(A) -0.5. P(ANB)...

    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)

  • Question 2: The sample space of a random experiment is fabedef) such that the prob- ability...

    Question 2: The sample space of a random experiment is fabedef) such that the prob- ability of each outcome is given in the following table: Outcome Probability 0.09 0.24 0.15 0.3 0.16 0.06 a. Consider the following events: C fa, c,d, f D-tb, d, e (a) What is the probability that event A occurs? (b) What is the probability that event D does not occur? (c) If event B occurs, what is the probability that event D occurs? (d) Are...

  • 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...

  • 4. Consider events A and B. Let C be the event that where either A occurs...

    4. Consider events A and B. Let C be the event that where either A occurs or B occurs, but not both. Show P(C)- P(A) P(B) - 2P(An B). Compute P(An B) and P(AlB) chance of being male. Let A the event that there is at most one female. Let B be 5. Consider events A and B. Suppose P(A)0.2, P(B)0.3 and P(AU B)-0.4. 6, A cat has a litter of kittens. Each kitten has a 50% chance of being...

  • 10. Suppose that A and B are mutually exclusive events for which P(A) 0.4,P(B) 0.3. The...

    10. Suppose that A and B are mutually exclusive events for which P(A) 0.4,P(B) 0.3. The probability that neither A nor B occurs equals a) 0.6 b) 0.1 c)0.7 d0.9

  • l. Suppose that A, B, and C are events such that PLA] = P[B] = 0.3,...

    l. Suppose that A, B, and C are events such that PLA] = P[B] = 0.3, P[C] = 0.55, P[An 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...

  • 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...

  • 1. (10 marks) (a) Let m events Bi, , Bm form a partition of the sample space Ω and let event A be...

    1. (10 marks) (a) Let m events Bi, , Bm form a partition of the sample space Ω and let event A be any event such that A c S2. Then show that given Bi > 0 for j = 1,.. ., m (b) Considcr a clinical trial where group of paticnts arc trcated for depression. As in many such trials a patient has two possible out- comes, in this study a relapse and no relapse. Refer to a relapse...

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