Math Problem Statement

95% sensitivity has been reported in the screening of cancer patients from non-cancer patients. In the previous study, with a probability of 0.4, people in the community are suffering from this type of cancer. If the result is positive for a person, the probability that the person will get cancer

Solution

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Math Problem Analysis

Mathematical Concepts

Bayes' Theorem
Conditional Probability
Probability Theory

Formulas

P(Cancer | Positive) = (P(Positive | Cancer) * P(Cancer)) / P(Positive)
P(Positive) = P(Positive | Cancer) * P(Cancer) + P(Positive | No Cancer) * P(No Cancer)

Theorems

Bayes' Theorem

Suitable Grade Level

Grades 11-12