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.
92
likes458 views
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
4.9114 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:
Frequently asked questions (FAQs)
What is the domain and range of the logarithmic function f(x) = log x and its natural logarithmic counterpart f(x) = ln x?
+
What is the definite integral of the function f(x) = 2x^3 + 3x^2 - 5x + 1 from x = -2 to x = 4 using the Fundamental Theorem of Calculus?
+
Math question: "Graph the inequality y > 2x - 3. Identify the shaded region using a dashed line for the boundary and shade above it.
+
New questions in Mathematics