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Understanding False Positives in Probability Testing

Explore the concept of false positives in probability testing using a practical example of HIV testing accuracy. Gain insights into calculating probabilities and distinguishing between true and false outcomes.

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Understanding False Positives in Probability Testing

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  1. Probability False Positives… Test Accuracy

  2. Given • 1/500 people have HIV • HIV test is 99% accurateWhat probabilities do you know?Consider the “nots”q = 1-p = p’

  3. P(HIV) = 1/500 • P’(HIV) = 1-(1/500) = 499/500 • Test 99% accurate meansP(test positive/ have HIV) = .99P(test negative/don’t have)

  4. Set up a tree !

  5. Add probabilities .99 .002 .01 .998 .01 .99

  6. Do all P(have HIV and test +)?.002*.99= .00198 .99 .002 .01 .01 .998 .99 All add up to 1

  7. Prob(B/A) = Prob(B)Prob(B/A)= P(AandB)/P(A) P(Not HIV and Test +) / Prob(TestPostive)= .00998/( .00998+.00198) = How can it be that high?

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