Multiplication Principle for Conditional Probabilities (example of medical test) The test for a certain medical condition is reasonably accurate, but not fully accurate. For an individual with the condition, the test is correct 90% of the time, giving a result of positive for 90% of these individuals and a result of negative for the other 10%. {As a conditional probability, this may be represented as P(+ | condition) = 0.9) and P(- | condition) = 0.1 } For those who do not have the condition, the test is correct 85% of the time giving a result of negative for 85% of these individuals and a positive result for the other 159 {As a conditional probability, this may be represented as P(+ | not condition) = 0.85) and P(- | not condition) = 0.15 } Use a tree diagram and the multiplication principle to answer the following questions. The first step in the tree diagram should be Condition vs Not Condition (with the probability given below). Then the second stage should be the test results, based on the conditional probabilities given above. a) first version Assume the condition is very common and 50% of the population has the condition, while 50% of the population does NOT have the condition. Use the tree diagram to find the probability of each of the following: P( + test and Condition) P( - test and Condition) {False negative} P( - test and NOT Condition) P( + test and NOT Conditon) {False positive} What portion of the positive tests are people who actually have the condition?
Multiplication Principle for Conditional Probabilities (example of medical test) The test for a certain medical condition is reasonably accurate, but not fully accurate. For an individual with the condition, the test is correct 90% of the time, giving a result of positive for 90% of these individuals and a result of negative for the other 10%. {As a conditional probability, this may be represented as P(+ | condition) = 0.9) and P(- | condition) = 0.1 } For those who do not have the condition, the test is correct 85% of the time giving a result of negative for 85% of these individuals and a positive result for the other 159 {As a conditional probability, this may be represented as P(+ | not condition) = 0.85) and P(- | not condition) = 0.15 } Use a tree diagram and the multiplication principle to answer the following questions. The first step in the tree diagram should be Condition vs Not Condition (with the probability given below). Then the second stage should be the test results, based on the conditional probabilities given above. a) first version Assume the condition is very common and 50% of the population has the condition, while 50% of the population does NOT have the condition. Use the tree diagram to find the probability of each of the following: P( + test and Condition) P( - test and Condition) {False negative} P( - test and NOT Condition) P( + test and NOT Conditon) {False positive} What portion of the positive tests are people who actually have the condition?
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Transcribed Image Text:QUESTION 10
Multiplication Principle for Conditional Probabilities
(example of medical test)
The test for a certain medical condition is reasonably accurate, but not fully accurate.
For an individual with the condition, the test is correct 90%
the time, giving a result of positive for 90% of these individuals and a result of negative for the other 10%.
{As a conditional probability, this may be represented as
P(+ | condition) = 0.9) and P(- | condition) = 0.1 }
For those who do not have the condition, the test is correct 85% of the time giving a result of negative for 85% of these individuals and a positive result for the other 15%.
{As a conditional probability, this may be represented as
P(+ | not condition) = 0.85) and P(- | not condition) = 0.15 }
Use a tree diagram and the multiplication principle to answer the following questions.
The first step in the tree diagram should be Condition vs Not Condition (with the probability given below).
Then the second stage should be the test results, based on the conditional probabilities given above.
a) first version
Assume the condition is very common and 50% of the population has the condition, while 50% of the population does NOT have the condition.
Use the tree diagram to find the probability of each of the following:
P( + test and Condition)
P( - test and Condition) {False negative}
P( - test and NOT Condition)
P( + test and NOT Conditon) {False positive}
What portion of the positive tests are people who actually have the condition?
b) second version with different frequency among populaiton
Assume the condition is not too common and 5% of the population has the condition, while 95% of the population does NOT have the condition.
Use the tree diagram to find the probability of each of the following:
P( + test and Condition)
P( - test and Condition) {False negative}
P( - test and NOT Condition)
P( + test and NOT Conditon) {False positive}
What portion of the positive tests are people who actually have the condition?
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