Diagnostic tests of medical condidtions have sereval results. the test results c
ID: 2931943 • Letter: D
Question
Diagnostic tests of medical condidtions have sereval results. the test results can be positive or negative, whether or not a patient actually has the condition. some patients without the condition might (inaccurately) test positive (called a "false positive"); other patients who do have the disease might slip through the diagnostic cracks and test negative (Called a 'false negative').
The table given here shows the results of 917 patients who took a preliminary diagnostic test, along with their eventual disease status.
Patient had the disease Patient did not have the disease
Test came back positive 40 185
Test came back negative 2 690
3) Please find P (Test was positive / Patient had the disease)
4) Please write a sentence interpreting your answer to question 3?
5) Please find P (patient had the disease / Test was postive)
6) Please interpret your answer to question 5.
Explanation / Answer
Ans:
We can calculate joint probabilty distribution,by dividing the each entry by 917:
3)P(test was positive/patient had the disease)=P(positive and disease)/P(disease)
=0.0436/0.0458
=0.9520
or P(test was positive/patient had the disease)=P(positive and disease)/P(disease)=40/42=0.952
4)Given that a patient actually has disease,there is probability that test will be positive is equal to 0.952
5)P (patient had the disease / Test was postive) =P(positive and disease)/P(positive)
=0.0436/0.2454=0.1778
or P (patient had the disease / Test was postive) =P(positive and disease)/P(positive)=40/225=0.1778
6)Given that a test was positive ,there is probability that patient has disease is equal to 0.1778
disease not disease Total Positive 40 185 225 Negative 2 690 692 Total 42 875 917 Joint probability distribution disease not disease Total Positive 0.0436 0.2017 0.2454 Negative 0.0022 0.7525 0.7546 Total 0.0458 0.9542 1