Earl's Decision Problem

# Earl's Decision Problem - Sample Test Question Earl had...

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Sample Test Question Earl had been experiencing dizziness, so his doctor ordered an MRI of his brain. The MRI revealed an inoperable tumor, but the MRI could not reveal if it was malignant or benign. In the population of patients like Earl, 10% turn out to be malignant. To obtain more information a biopsy of the tumor is needed. A "positive" biopsy result means that the tumor is malignant. The false positive rate is 10%, while the false negative rate is 1%; in other words, the biopsy of benign tumors is positive 10% of the time, while the biopsy of malignant tumors is negative 1% of the time. a) Solve for the probability that Earl has a malignant tumor conditional on having a positive biopsy result. b) Solve for the probability that Earl has a malignant tumor conditional on having a negative biopsy result. c) Solve for the unconditional probability of a positive biopsy result. For simplicity, assume the outcome space is {living a normal life without chemotherapy, living a normal life with chemotherapy, and dying prematurely}.
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