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b) P(An B) ent patients at a dentist\'s office concerning fear of visiting the d

ID: 3051276 • Letter: B

Question

b) P(An B) ent patients at a dentist's office concerning fear of visiting the dentist suggest the following proportions Elementary Middle High School 0.12 0.28 SchoolSchool 0.08 0.25 Fear Do not fear 0.05 0.22 For a student selected at random, consider the events A-[Fear and M[Middle School, Find the probabilities P(A).PA n M),PM).P(AU M).A)2 Are A and M independent? Why or why not? a) b) 3) in a region, 12% of the adult population are smokers, 0.8% are smokers with emphysema, and 0.2% are nonsmokers with emphysema. Denote the events A as the selected person is a Smoker and B as the selected person has emphysema a) What is the probability that a person selected at random has emphysemar b) Given that the selected person is a smoker, what is the probability that this person has emphysema? c) Given that the selected person is not a smoker, what is the probability that this person has emphysema? 4) Suppose P(A)-0.6 and P(B)-0.22 a) Determine P(A U B) if A and 8 are independent. b) Determine P(A U B) if A and B are mutually exclusive. c) Find P(AlB) if A and B are mutually exclusive. 5) Let A the event that a person is a moderate or heavy drinker and B the event that the person is a female. For a person selected at random in the United States, the probabilities are: P(B)= 0.50, p(AIB)= 0.12, PCAIB) 0.29 a) b) c) Express in words, in the context of this problem, the third probability statement. Determine the probability that the person selected is a moderate or heavy drinker. If the person selected is found to be a moderate or heavy drinker, what is the probability of being female

Explanation / Answer

5

a) P(A/B bar) = Probability that a person is moderate or heavy drinker given that the person is not female (as we are using B bar)

b)

P(Person selected is moderate or heavy drinker)

= P(A) = P(A/B) + P(A/B bar)

= 0.12+0.29

= 0.41

c)

If person is moderate or heavy drinker then probability that person is female

= P(B/A)

=P(A/B)*P(B) / P(A)

=0.12*0.50/0.41

= 0.146