Question
From a group of patients infected by respiratory diseases. 47 suffer from asthma, 33 patients suffer from asthma and chronic cough, 61 patients suffer from pneumonia, 62 suffer from chronic cough, 31 patients suffer from asthma and pneumonia, 21 suffer from asthma, chronic cough and pneumonia. Represent the information provided in a Venn diagram and find the number of patients who: to. They suffer from asthma or a chronic cough, but not both. b. They suffer from chronic cough, but do not suffer from asthma or pneumonia. C. They suffer from two respiratory diseases. d. They suffer only from a respiratory disease.
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Answer to a math question From a group of patients infected by respiratory diseases. 47 suffer from asthma, 33 patients suffer from asthma and chronic cough, 61 patients suffer from pneumonia, 62 suffer from chronic cough, 31 patients suffer from asthma and pneumonia, 21 suffer from asthma, chronic cough and pneumonia. Represent the information provided in a Venn diagram and find the number of patients who: to. They suffer from asthma or a chronic cough, but not both. b. They suffer from chronic cough, but do not suffer from asthma or pneumonia. C. They suffer from two respiratory diseases. d. They suffer only from a respiratory disease.
Miles
4.9115 Answers
a. Number of patients who suffer from asthma or a chronic cough, but not both:
|A - B| + |B - A|
|A |+ |B| - 2|A \cap B|
= 47 + 62 - 2 \times 33
= 43 \text{ patients}
b. Number of patients who suffer from chronic cough, but do not suffer from asthma or pneumonia:
|B - (A \cup C)
= |B| - |B \cap A| - |B \cap C| + |A \cap B \cap C|
= 62 - (33 + 10 - 10)
= 29 \text{ patients}
c. Number of patients who suffer from two respiratory diseases:
( |A \cap B - C| + |B \cap C - A| + |A \cap C - B|)
= (33 - 21) + (33 - 21) + (31 - 21)
= 7 + 12 + 10
= 29 \text{ patients}
d. Number of patients who suffer only from one respiratory disease:
( |A - (B \cup C)| + |B - (A \cup C)| + |C - (A \cup B)|)
= (47 - 33 - 31 + 21) + |B - (A \cup C)| + (61 - 31 - 33 + 21)
= 4 + 29 + 18
= 51 \text{ patients}
b. Number of patients who suffer from chronic cough, but do not suffer from asthma or pneumonia:
c. Number of patients who suffer from two respiratory diseases:
d. Number of patients who suffer only from one respiratory disease:
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