6. Consider en experiment and two events A and B and their complements. The probability of the union of events A and B is precisely 3/4. Moreover, some other probabilities are summarized as follows: A B Bc 3/8 Ac 1/8] (a) Describe the following event in terms of a union or intersection and find their prob- abilities: (i) A is observed and B is not observed. (ii) A is not observed or B is observed. (iii) B is not observed. (b) Assume that event B is observed. What is the probability that A is observed? What is the probability that A is observed assuming Bº is observed? (c) Are A and B independent?

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6. Consider en experiment and two events A and B and their complements. The probability
of the union of events A and B is precisely 3/4. Moreover, some other probabilities are
summarized as follows:
A Ac
1/8]
B
Bc 3/8
(a) Describe the following event in terms of a union or intersection and find their prob-
abilities:
(i) A is observed and B is not observed.
(ii) A is not observed or B is observed.
(iii) B is not observed.
(b) Assume that event B is observed. What is the probability that A is observed?
What is the probability that A is observed assuming Bº is observed?
(c) Are A and B independent?
Transcribed Image Text:6. Consider en experiment and two events A and B and their complements. The probability of the union of events A and B is precisely 3/4. Moreover, some other probabilities are summarized as follows: A Ac 1/8] B Bc 3/8 (a) Describe the following event in terms of a union or intersection and find their prob- abilities: (i) A is observed and B is not observed. (ii) A is not observed or B is observed. (iii) B is not observed. (b) Assume that event B is observed. What is the probability that A is observed? What is the probability that A is observed assuming Bº is observed? (c) Are A and B independent?
Expert Solution
Step 1

Given that:

  A Ac
B   18
Bc 38  

Union of A and B is, AB=34

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