A doctor is trying to determine if a patient has one of three diseases, d1, d2, or d3 ...

        A doctor is trying to determine if a patient has one of three   diseases, d1, d2, or d3. two tests are administered. each test result is   classified as either positive or negative. therefore there are four test   patterns: ++, + -, - +, - -. The data in the table gives the results for   10,000 people having one of the three diseases.   Disease   Number having disease Test pattern       + + + - - +   - -         d1 3,215 2,   110 301 704 100        d2 2,125 396   132 1187 410        d3     4660 510 3568 73 509        a. construct   a tree diagram with two stages. let the four test patterns compose the first   stage. write probabilities along each of the branches   b. find   P(d1), P(d2), P(d3)        c. find the   probability that a randomly chosen patient has disease d2 if the test result   show a - + pattern