Consider a diagnostic test for cancer that is 99% accurate on individuals with c

Question

Consider a diagnostic test for cancer that is 99% accurate on individuals with cancer (i.e. if an individual has cancer, the test is 99% likely to produce a positive test). it is 90% accurate for individuals without cancer, i.e. it produces a negative result for 90% of healthy individuals. this test is then applied to a population where the prevalence of cancer is 0.01 (1%). if an individual receives a positive test, what is the probability that the tested patient has cancer? *Note probability is a decimal number between zero and 1, not a percent.

Explanation / Answer

              Individual has cancer       Individual does not have cancer                 Total

Diagnostic test positive           0.99 X 0.99= 0.9801                   0.01-0.009=0.001                     0.9811

Diagnostic test negative           0.99 - 0.9801 = 0.0099           0.01 X 0.90 = 0.009                      0.0189

Total                                       0.99                                   0.01                                              1.00

So,

P(Individual has cancer/Dianostic test positive) = P(Individual has cancer & Diagnostic test positive)/ P(Diagnostic test positive)

= 0.9801/0.9811 = 0.9990

So,

Answer is:

0.9990

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.