Suppose that 10 people need to be tested for a widespread viral flu. Assume that each person has a 8% chance of having the virus, independently from person to person. Consider two different plans for conducting the tests: • Plan A: Give one test to each person.
Suppose that 10 people need to be tested for a widespread viral flu. Assume that each person has a 8% chance of having the virus, independently from person to person. Consider two different plans for conducting the tests: • Plan A: Give one test to each person.
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Suppose that 10 people need to be tested for a widespread viral flu. Assume that each person has a 8% chance of having
the virus, independently from person to person. Consider two different plans for conducting the tests:
* Plan A: Give one test to each person.
* Plan B: Combine/mix the test samples from all 10 people into one batch. Then test that batch:
> If at least one person has the virus, then the test result of the batch will be positive, and all 10 people will
then need to be tested individually.
> If nobody has the disease, then the batch test result will be negative, and no additional tests will be needed.
Let the random variable X represent the total number of tests needed with Plan B (batch testing).
a) Determine the probability distribution (probability model) of X.
b) Determine the expected value of X.
c) Interpret what the expected value means in this context.
d) If you had to test thousands of groups of 10 people, which plan - A or B- is better? Explain your reasoning.
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