Examples of Conditional Probabilities, Marginal Totals, and Bayes Theorem Book Example 4, Section 4-3 Positive Test Result Negative Test Result (positive) (negative) Cancer 8 2 C (true positive) (false negative) No Cancer 99 891 C (false positive) (true negative) The table is summarized and the marginal totals calculated below. From the marginal totals can be calculated any desired conditional probability. positive negative total C 8 2 10 Ppositive|C 8 /10 .8 C 99 891 990 Ppositive|C 99 / 990 .1 total 107 893 1000 P C | positive 8 /107 .0748 P(positive)=107/1000=.107 P C 10 /1000 .01 P C 990 /1000 .99.

the HomeWork Quesntions are: Refer to the table which summarizes the results of testing for a certain disease. Positive Negative Test Result Test Result Subject has the disease 111 4 Subject does not have the disease 11 172 a. In the table, calculate all 5 marginal totals. b. If a result is negative, what is the probability that it is a false negative (test indicates the person does not have the disease when in fact they do)? HINT: This is a conditional probability and will involve a marginal total. c. If a result is positive, what is the probability that it is a false positive (test indicates the person does have the disease when in fact they don't)? HINT: This is a conditional probability and will involve a marginal total. Extra Credit: 7. Suppose subjects with a particular disease test positive 98% of the time, and subjects without the disease test positive 4% of the time. 10% of the subjects have the disease. Given that a subject tests positive, what is the probability that they have the disease? HINT: Use Bayes' Rule