Part 2: Cogscitis

You wake up with a feeling of total bliss and an irresistible desire to read about cognitive science. You go to the health center where both Doctor A and Doctor B independently (i.e. you have separate appointments with each of them) consider the possibility that you have cogscitis, a brain condition caused by a virus.

Doctor A gives the hypothesis that you do have cogscitis a prior probability of 0.70 (so, the prior probability of the not-cogscitis hypothesis is 0.3). Doctor B gives the cogscitis hypothesis a prior probability of 0.20.

The doctors each order three tests, and the results come back sequentially: the results of test 1 come back first, the results of test 2 come back second, and the test 3 results come back third. The Doctors both engage in Bayesian updating after seeing the results of each test.

Test 2 comes back next and it is positive. Here are the likelihoods for the positive result for Test 2:

Hypothesis	Probability of positive test result given hypothesis
cogscitis	0.60
not cogscitis	0.20

Hint: Use your posterior probability after seeing the results of Test 1 as your new prior probability, before seeing the results of Test 2.

NOTE:Your numerical answers should all be reported as probabilities, not percentages, and should be rounded to two decimal places.

1.Now given your positive test result from Test 2, what is Doctor B's posterior probability for the hypothesis that you DO have cogscitis? Round your answer to two decimal places.

Test 3 comes back next and it, too, is positive. Here are the likelihoods for the positive result for Test 3.

Hypothesis	Probability of positive test result given hypothesis
cogscitis	0.90
not cogscitis	0.10

Hint: Use your posterior probability after seeing the results of Test 2 as the new prior probability, before seeing the results of Test 3.

NOTE:Your numerical answers should all be reported as probabilities, not percentages, and should be rounded to two decimal places.

1.Now given your positive test result from Test 3, what is Doctor A's posterior probability for the hypothesis that you DO have cogscitis? Round your answer to two decimal places.

2. Now given your positive test result from Test 3, what is Doctor B's posterior probability for the hypothesis that you DO have cogscitis? Round your answer to two decimal places.