Question 1047065: 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 Result
Positive Negative
Cancer Present 0.21 0.79
Cancer Absent 0.06 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 6.4% of the population has prostate cancer. What is the probability that a person does not have cancer, given that the PSA test is positive? This is the false-positive rate. (Round your answer to five decimal places.)
P =
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! ========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
|
|
|
