Solution Found!
To determine whether they have a certain disease, 100
Chapter 4, Problem 32P(choose chapter or problem)
Problem 32P
To determine whether they have a certain disease, 100 people are to have their blood tested. However, rather than testing each individual separately, it has been decided first to place the people into groups of 10. The blood samples of the 10 people in each group will be pooled and analyzed together, if the test is negative, one test will suffice for the 10 people, whereas if the test is positive, each of the 10 people will also be individually tested and, in all, 11 tests will be made on this group. Assume that the probability that a person has the disease is .1 for all people, independently of one another, and compute the expected number of tests necessary for each group.
Questions & Answers
QUESTION:
Problem 32P
To determine whether they have a certain disease, 100 people are to have their blood tested. However, rather than testing each individual separately, it has been decided first to place the people into groups of 10. The blood samples of the 10 people in each group will be pooled and analyzed together, if the test is negative, one test will suffice for the 10 people, whereas if the test is positive, each of the 10 people will also be individually tested and, in all, 11 tests will be made on this group. Assume that the probability that a person has the disease is .1 for all people, independently of one another, and compute the expected number of tests necessary for each group.
ANSWER:
Solution:
Step 1 of 2:
A blood samples of 10 people in each group will be pooled and analyzed together, if the test is negative, the we will stop it, whereas if the test is positive, each of the 10 people will also be individually tested and, in all 11 tests will be made on this group.
The probability that a person has disease is 0.1.
We have to compute the expected number of tests necessary for each group of 10 people.