QUESTUON 2 - 30 MARKSIn an experiment, A,B,C, and D are events with probabilities P[A]=2/8, P[B]=3/24, P[C]=15/24, andP[D]=9/24. Furthermore, A and B are disjoint while C and D are independent. CalculateA. P[AOB]В. Р[AUB].C. P[AOB“].D. P[AUB].E. Are A and B independent?F. P[CND].G. P[CU D} .H. P[C°nD°].P[CUD ].J. Are C and D independent?1.3 marks each

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Answered: In an experiment, A,B,C, and D are…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Given P(A) = 0.21, P(B) = 0.99, P(C) = 0.31 and that events A, B, and C are independent, what is P(A, B, and C).
Suppose that E and F are two events and that P(E and F) = 0.2 and P(E) = 0.5. What is P(F|E)? ... P(F|E) = (Type an integer or a decimal. Do not round.)
Dr. Cy Clopps is ophthalmologist and owner of the Spex Appeal Eye Clinic. A review of 100 patient’s records indicated that 30 of these patients have vision insurance. Further, 35 of the 100 patients got bifocal glasses but had no insurance. Finally, 10 of the 100 patients had insurance but did not get bifocals. d. Of those with insurance, what proportion got bifocals? e.Are the events independent? Mutually exclusive? Collectively exhaustive?
If P (Event A)=0.2 and P(Event B)=0.3, and the two events are disjoint, then P (Event A and Event B) is?
In an experiment, A, B,C, and D are events with probabilities P[A] = 2/8, P[B]= 3/24, P[C] =15/24, and P[D]=9/24. Furthermore, A and B are disjoint while C and D are independent. Use this information to answer the questions below.
Suppose that we have two events, A and B, with P(A) = .70, P(B) = .60, and P(A N B) = .40. a. Find P(A | B) (to 4 decimals). b. Find P(B | A) (to 4 decimals). c. Are A and B independent? Why or why not? Select v because P(A | B) is Select P(A).
Given P(A) = 0.34, P(B) = 0.60, P(C) = 0.21 and that events A, B, and C are independent, what is P(A, B, and C).
10 . Let A, B be independent events with P (A) = P (B) = 1/3. Find the probability that exactly one of the two will occur: Select one : a. 4/9 b. 1/9 c. 1/3 d. 2/9
Given P(A) = 0.18; P(B) = 0.51 , P(C) = 0.36 and that events A , B, and C are independent, what is P(A,B) and C)
4. 60% of homeowners in Northern Virginia have a weekly lawn service. Those homes with a lawn service, 55% have a sprinkler system. For those without a lawn service, 30% have a sprinkler system. (Note: you do NOT need to simplify these answers. However, you MUST express each in terms of the events/probability notation – e.g., P(A|B) =..) a. Draw a tree diagram to model the problem b. What is the probability that a randomly selected home has a sprinkler system? c. What is the probability that a randomly selected home with a sprinkler system has a lawn service? d. What is the probability that a randomly selected home with a lawn service has a sprinkler system? e. What is the probability that a randomly selected home has a lawn service? f. What is the probability that a randomly selected home that does not have a lawn service has a sprinkler system?

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In an experiment, A,B,C, and D are events with probabilities P[A]=2/8, P[B]=3/24, P[C]=15/24, and P[D]=9/24. Furthermore, A and B are disjoint while C and D are independent. Calculate A. P[AOB] B. P[AUB]. C. P[ANB].