Question

To prevent developing a certain type of cancer, Health Canada organize a diagnostic test. The false positive and negative rates for this diagnostic test are five percent and four percent, respectively. Assume that five percent of the population has this type of cancer.

1. If a randomly selected person has a positive test result, what is the probability that the person has this type of cancer
2. The test is administrated twice on the same patient. Assume that the test results are independent from each other, conditionally on the patient’s disease status. given that both the test results were positive, what is the probability that the patienet has this type of cancer

Answer 1

solution :- bula C: Has concer T: Test positive P (c) = 0.05 PIDE .) 0.05 сс PC ) = 0.04 P(t) = plu. p(69+ (1-P119. PCD リ BeF2 0.05 80.95 + (1-0.04) X0.05 Now, = 0.0955 PG) PID.PLG 11-0.06x0.05 - PIT) 81 0.0955 = 0.5026 Woh For ) PL TOT).PO PO TOT). P10)+1 Plano). POS 2 (1-0.04J xo.o5 1-0.041 2xo.os + 10.05) 2x0.95 =lo.9510