Q 28. Pnuemonia and Bronchitis: Show your work and explain your answ proper probability notation. Answers (even correct ones) without justification receive marks. Among 50 patients admitted to a hospital, 25 are diagnosed with p nia, 30 patients have bronchitis, and 10 of them are diagnosed w pneumonia and bronchitis. a) Show this information on a Venn diagram. Be sure to define any events you and clearly label the Venn diagram. b) If one of these patients is randomly selected, what is the probability the selecte has both pneumonia and bronchitis?

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Q 28. Pnuemonia and Bronchitis: Show your work and explain your answers. Use
proper probability notation. Answers (even correct ones) without justification will not
теceive marks.
Among 50 patients admitted to a hospital, 25 are diagnosed with pneumo-
nia, 30 patients have bronchitis, and 10 of them are diagnosed with both
рпеumonia and bronchitis.
a) Show this information on a Venn diagram. Be sure to define any events you introduce
and clearly label the Venn diagram.
b) If one of these patients is randomly selected, what is the probability the selected patient
has both pneumonia and bronchitis?
c) Amongst all patients with bronchitis, what percentage also have pneumonia?
d) If two of these patients are randomly selected, what is the probability that both of the
selected patients have pneumonia but not bronchitis?
e) Are having bronchitis and having pneumonia independent events? Answer YES or NO
and give statistical justification.
f) Are having bronchitis and having pneumonia mutually exclusive events? Answer YES
or NO and give statistical justification.
g) Is it possible for 4 of these patients to have COPD (Chronic Obstructive Pulmonary
Disease), but not have either pneumonia or bronchitis? Answer YES or NO and give
statistical/numerical justification.
Transcribed Image Text:Q 28. Pnuemonia and Bronchitis: Show your work and explain your answers. Use proper probability notation. Answers (even correct ones) without justification will not теceive marks. Among 50 patients admitted to a hospital, 25 are diagnosed with pneumo- nia, 30 patients have bronchitis, and 10 of them are diagnosed with both рпеumonia and bronchitis. a) Show this information on a Venn diagram. Be sure to define any events you introduce and clearly label the Venn diagram. b) If one of these patients is randomly selected, what is the probability the selected patient has both pneumonia and bronchitis? c) Amongst all patients with bronchitis, what percentage also have pneumonia? d) If two of these patients are randomly selected, what is the probability that both of the selected patients have pneumonia but not bronchitis? e) Are having bronchitis and having pneumonia independent events? Answer YES or NO and give statistical justification. f) Are having bronchitis and having pneumonia mutually exclusive events? Answer YES or NO and give statistical justification. g) Is it possible for 4 of these patients to have COPD (Chronic Obstructive Pulmonary Disease), but not have either pneumonia or bronchitis? Answer YES or NO and give statistical/numerical justification.
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