1. Suppose you are the head of a laboratory that tests for a certain rare condit

Question

1. Suppose you are the head of a laboratory that tests for a certain rare condition. Your test is pretty good: given that a patient actually has the condition, the patient will (correctly) test positive 99% of the time! There are also very few false negatives: given that a patient does not have the condition, they will (correctly) test negative 98% of the time. However, the condition is very rare; only .1% of all people have this condition. So, given that someone tests positive, what is the probability that they actually have the condition? 2. Suppose you are taking an exam that adjusts its difficulty on later questions based on how well you do on previous questions. This exam has only two problems. The first problem is medium difficulty: you think you have only a 65% chance of answering it correctly. If you get the first problema correct then it asks a more difficult question that you have a 40% chance of answering correctly. On the other hand, if you answer the first question incorrectly, then it will ask an easier question that you havea 85% chance of answering correctly. What is the probability that you answer the second question correctly?

Explanation / Answer

(1)

P(Has the disease | Tests positive) = 0.00099/0.02097 = 0.0472

Tests positive Tests negative Total Has the disease 0.99 * 0.001 = 0.00099 0.001 - 0.00099 = 0.00001 0.001 Does not have the disease 0.999 - 0.97902 = 0.01998 0.98 * 0.999 = 0.97902 0.999 Total 0.02097 0.97903 1

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