A researcher wanted to compare the diagnostic results (Yes=tumor present, No=tumor not present) from a pathologist with that obtained from a physician on the same 147 patients. The following table shows the frequencies of results from two different sources.
Pathologist
Physician | Pathologist result = Yes | Pathologist result = No | Total
Physician result = Yes | 34 | 27 | 61
Physician result = No | 15 | 71 | 86
Total | 49 | 98 | 147
Leave your answers to Q1 to Q4 as fractions – you should NOT reduce/simplify them and/or convert them to decimals/percentages.
1. What is the probability of a “No” result from the pathologist?
2. What is the probability that the physician says “No” *and* the pathologist says “Yes”?
3. What is the probability that the physician says “No” *given* that the pathologist says “Yes”?
4. What is the probability that the physician and the pathologist agree in their conclusion? (“Agree” means both say Yes *or* both say No.)
5. Are the physician and pathologist results independent – show some work; not just a yes/no answer? (When conducting a test of independence, each possible joint probability must equal the product of its respective marginal probabilities. If any are not equal then there is not independence.)
6. Draw a two-circle Venn diagram with the data in this question. Your rectangle (sample space S) will contain all patients. Make one event circle for “Path=N”, make another event circle for “Phys=N” – they will intersect since there are patients who had both Path and Phys = No. Indicate the correct count in each part of your diagram ... these counts must add to 147.