Question

2 multiple choice 1 point
among a group of students, 49 study physics, 37 study english and 21 study biology. if 9 of these students study physics and english, 5 study english and biology, 4 study physics and biology and 3 study physics, english and biology, find the number of students in the group.
92
86
none of these
91
3 fill in the blank 2 points
among 50 patients admitted to a hospital, 25 are diagnosed with pneumonia, 30 with bronchitis, and 10 with both pneumonia and bronchitis. create a venn diagram and use the principle of inclusion - exclusion to determine:
(a) the number of patients diagnosed with pneumonia or bronchitis (or both). type your answer...
(b) the number of patients not diagnosed with pneumonia or bronchitis. type your answer...

Explanation:

Question 2

Step1: Apply the principle of inclusion - exclusion

The formula for \(n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(A\cap C)-n(B\cap C)+n(A\cap B\cap C)\)
Let \(A\) be the set of students studying Physics (\(n(A) = 49\)), \(B\) be the set of students studying English (\(n(B)=37\)), and \(C\) be the set of students studying Biology (\(n(C) = 21\)). Also, \(n(A\cap B)=9\), \(n(B\cap C)=5\), \(n(A\cap C)=4\), and \(n(A\cap B\cap C)=3\)

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Step1: Apply the principle of inclusion - exclusion

Let \(A\) be the set of patients with pneumonia (\(n(A)=25\)) and \(B\) be the set of patients with bronchitis (\(n(B) = 30\)), and \(n(A\cap B)=10\)
The formula for \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\)

Step2: Substitute the values

$$
LATEXBLOCK0
$$

Step1: Use the total number of patients

The total number of patients \(N = 50\)
The number of patients with pneumonia or bronchitis (or both) is \(n(A\cup B)=45\) (from part (a))

Step2: Calculate the number of patients not diagnosed

The number of patients not diagnosed with pneumonia or bronchitis is \(N-n(A\cup B)\)

$$
LATEXBLOCK0
$$

Answer:

92

Question 3

Part (a)