Answered: Researchers discover that 85% of people…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.8: Probabilities Of Disjoint And Overlapping Events

Problem 2C

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Researchers discover that 85% of people who have suffered a heart attack had periodontal disease (an inflammation of the gums). Only 29% of people that have not had a heart attack actually have periodontal disease.

a. Suppose heart attacks are rare in a community, occurring with a 10% probability. What is the probability that someone has periodontal disease?

b. What is the probability that a person with periodontal disease will have a heart attack?

Expert Solution

Given

$\begin{array}{rcl} P (h e a r t a t t a c k) & = & 0.10 \\ ∴ P (n o h e a r t a t t a c k) & = & 1 - P (h e a r t a t t a c k) \\ = & 1 - 0.10 \\ = & 0.90 \\ A l s o, \\ P (d i s e a s e | h e a r t a t t a c k) & = & 0.85 \\ ∴ P (n o d i s e a s e | h e a r t a t t a c k) & = & 1 - 0.85 \\ = & 0.15 \\ A n d P (d i s e a s e | n o h e a r t a t t a c k) & = & 0.29 \\ ∴ P (n o d i s e a s e | n o h e a r t a t t a c k) & = & 1 - 0.29 \\ = & 0.71 \end{array}$

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