
Concept explainers
a.
To graph: The Venn diagram that represents the number of patients of lung cancer and patients of chronic smokers.
a.

Explanation of Solution
Given information:
The number of patients diagnosed with lung cancer are 40, number of patient who are chronic smokers are 30. 25 patients have both lung cancer and smoke.
Graph:
Consider the information that the number of patients diagnosed with lung cancer are 40, number of patient who are chronic smokers are 30. 25 patients have both lung cancer and smoke.
Let A represents the patient only with lung cancer.
So,
Let C represents only the chronic smoker patients.
So,
The Venn diagram that represent the situation is
The portion A represents the patient only with lung cancer.
The portion C represents only the chronic smoker patients.
The portion B represents the both that is patients have both lung cancer and smoke.
Interpretation:
The sum total of portion A and B is equal to patient with lung cancer. The sum total of portion B and C is equal to chronic smoker patients.
b.
To calculate: The probability that patient has lung cancer provided that patient smokes.
b.

Answer to Problem 38E
The probability that patient has lung cancer provided that patient smokes is
Explanation of Solution
Given information:
The number of patients diagnosed with lung cancer are 40, number of patient who are chronic smokers are 30. 25 patients have both lung cancer and smoke.
Formula used:
Probability of an event E is
Given an event Q, the conditional probability of event A is
Calculation:
Consider the provided information that the number of patients diagnosed with lung cancer are 40, number of patient who are chronic smokers are 30. 25 patients have both lung cancer and smoke.
Total number of patients are 200.
Let A be an event that patient has lung cancer and B be an event that patient smokes.
Recall that probability of an event E is
Probability that patient smokes,
Probability that patient has lung cancer and patient smokes,
Recall that given an event Q, the conditional probability of event A is
The probability that patient has lung cancer provided that patient smokes.
Thus, the probability that patient has lung cancer provided that patient smokes is
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