A scientist is studying the relationship between stomach aches and headaches among students. On her survey, she asked if the participant had headaches that could be classified as “sudden,” “chronic,” or “none.” The survey also asked if the participant had stomach aches with answers of “yes” or “no.” From the survey she found:14% have sudden headaches;22% have chronic headaches;15% have stomach aches;Of those with stomach aches, 1⁄3 have sudden headaches.Of those with no headaches, 1⁄8 have stomach aches.What is the probability that a randomly selected student from the survey did not have stomach aches, but they do have chronic headaches?

Answered: scientist is studying the relationship…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

A scientist is studying the relationship between stomach aches and headaches among students. On her survey, she asked if the participant had headaches that could be classified as “sudden,” “chronic,” or “none.” The survey also asked if the participant had stomach aches with answers of “yes” or “no.” From the survey she found:

14% have sudden headaches;
22% have chronic headaches;
15% have stomach aches;
Of those with stomach aches, 1⁄3 have sudden headaches.
Of those with no headaches, 1⁄8 have stomach aches.

What is the probability that a randomly selected student from the survey did not have stomach aches, but they do have chronic headaches?

Expert Solution

Step 1

Given that headaches could be classified as "sudden", "chronic", or "none". The survey also asked if the participant had stomach aches with answers of "yes" or "no".

From the survey she found:

14% have sudden headaches;
22% have chronic headaches;
15% have stomach aches;
Of those with stomach aches, 1⁄3 have sudden headaches.
Of those with no headaches, 1⁄8 have stomach aches.

So,

$P (sudden headaches) = 0.14 P (chronic headaches) = 0.22 P (stomach aches) = 0.15 P (sudden headaches|stomach aches) = \frac{1}{3} P (stomach aches|no headaches) = \frac{1}{8}$

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