The prostate-specific antigen (PSA) test is a simple blood test to screen for pr
ID: 2922633 • Letter: T
Question
The prostate-specific antigen (PSA) test is a simple blood test to screen for prostate cancer. It has been used in men over 50 as a routine part of a physical exam, with levels above 4 ng/mL indicating possible prostate cancer. The test result is not always correct, sometimes indicating prostate cancer when it is not present and often missing prostate cancer that is present. Suppose that these are the approximate conditional probabilities of a positive (above 4 ng/ml) and negative test result given cancer is present or absent. Test Resulit Positive Negative Cancer present 0.21 Cancer absent0.06 0.79 0.94 Draw a tree diagram for selecting a person from this population (outcomes: cancer present or absent) and testing his blood (outcomes: test positive or negative) Suppose that 6.6% of the population has prostate cancer, what is the probability that a person does not have cancer, given that the PSA test is positive? (Round your answer to five decimal places.) P=0.80155 XExplanation / Answer
Solution:
=======T+========T-=====Total
C+======1344=====5056====6400
C-====== 5616=====87984==93600
total=== =6960====93040===100000
This puts the data into numerical form for a population of 100,000, without decimals.
Tree diagram
person------------C+---------TP-- 1.3%
-------------------------------TN--5.1%
============= C-----------TP -5.6%
-------------------------------TN-88.0%
Given that the test is positive (6960),
the probability that they do not have cancer is (5616/6960)=0.80690
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.