Question

The table below shows the predicted testing outcome for a disease that affects 2% of a population, and has 90% accuracy rate. Positive Test Negative Test Total Has Disease 18 2 20 Does Not Have Disease 98 882 980 Total 116 1000 884 Given you received a positive test, w he probability that you do not have the disease? Write your answer as a percentage, rounded to the nearest tenth of a percent.

Answer 1

Negative Test Total 2 20 Has Disease Does Not Have Disease Total Positive Test 18 98 116 882 980 884 1000

2-1: disease of the population testing. 90% il affected by the has acwacy rate. be let has probability that a benson PLAL the disease. so PLAI= 20 = 0.02 let P(B be P(B) = the boobability 116 o.126 of positive test, 80 looo We he find the probability of disease (Al green that the patient has a positive test. Find P(A/B) Using Bayes's Theoler PLA/B) = P(B/4) PLA). PLB) Since accurate, lo test PIBLA) 18 900:41 0.9 Therefore P(A/B) = 2 o.9 Xo-02 0.116 0.018 0.116 0.155172414

lace a Mou probability that you don't disease green a positive test (1 - P(AB) x P(B) IPCA) Cl-o: 155172414) X 0.116 0.02 0.098 0.98 o ! So there you don't seceiving O'lX100 have the positive test chances that disease white
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