You wake up with a feeling of total bliss and an iresistible desire to read about cognitive science. You go to the health center tne possbility of cogscitis, a brain condion due to a vinus Doctor A gives his where Doctor A and Doctor B consider hypothesis a prioe probability of 0.70 (thus.30 They order three tests and the results second, and test 3 third. They engage in Bayesian updating ater seing the results of Test 1 comes back fest ard isposto. Here are the likelroods tor the postive probability for NOT cogsctisi while gives it a prior probability of 0.20 thus 0 80 probability for NOT cogscitis crno back sequertany test 1 first, test 2 result for Test 1 cogscitis0.70 not cogsotis 0.10 Us ng Bayes. rde, calculate the postenor probabites arrived by each doctor for hypothesis that you DO have oogscitis After Test 1, what is Doctor A's posterior probablity for the hypothesis that you DO have oogscitis? eet 1. what is Doctor B's posterior probability for the hypothesis that you DO harve cogscitis? Test 2 comes back next and it is positive. Here are the lkelihoods for the positive result for Test 2: Probability. of positve cogscitis 0.60 not cogscitis 0.20 Using Bayes' rule, update the posterior probabilities arrived at by each doctor for the hypothesis that you DO have cogscitis. Hint: Use your posterior probability after seeing the results of Test 1 as the prior probability before seeing the results of Test 2 After Test 2, what is Doctor A's posterior probability for the hypothesis that you DO have cogscitis? After Test 2, what is Doctor B's posterior probability for the hypothesis that you DO have cogscitis? Test 3 comes back next and it is positive. Here are the likelhoods for the positive result for Test 3 cogscitis 0.90 not cogscitiso.10 Using Bayes' rule, update the posterior probabilities arrived at by each doctor for the hypothesis that you DO have cogscitis. Hint: Use your posterior probability after seeing the results of Test 2 as the prior probability before seeing the results of Test 3 After Test 3, what is Doctor A's posterior probability for the hypothesis that you DO have cogscits? After Test 3, what is Doctor B's posterior probability for the hypothesis that you DO have cogscitis?