On the basis of a physical examination, a doctor determines theprobability of no tumour (event labelled C for‘clear’), a benign tumour (B) or a malignant tumour (M) as 0.7, 0.2and 0.1 respectively.
A further, in depth, test is conducted on the patient which canyield either a negative (N) result or positive (P). The test givesa negative result with probability 0.9 if no tumour is present(i.e. P(N|C) = 0.9). The test gives a negative result withprobability 0.8 if there is a benign tumour and 0.2 if there is amalignant tumour.
(i) Given this information calculatethe joint and marginal probabilities and display in the tablebelow.
| Positive (P) | Negative (N) | MP |
Clear (C) | 0.07 | 0.63 | 0.7 |
Benign (B) | 0.04 | 0.16 | 0.2 |
Malignant (M) | 0.08 | 0.02 | 0.1 |
MP | 0.19 | 0.81 | 1 |
- Obtain the posterior probability distribution for the patientwhen the test result is
a) positive, b) negative
- Comment on how the test results change the doctor’s view of thepresence of a tumour.
