Travels around my prostate

Since the cab had to be either white or silver, the total probability of it being identified as silver, whether right or wrong, is .12 + .17 = .29. In other words, this witness could be expected to identify the cab as silver 29% of the time whether he was right or wrong.

The chances he was right are .12 out of .29, or 41% which I would suggest is much lower that people would expect.

Let us now move from the hypothetical to the practical. Every six months I go to the doctors to get my recharge of amlodipine, diabex, irbesartan, and rosuvastatin. Just prior to the visit I have a blood test. I do this visit at the time of the equinox and in October 2013 my PSA reading had jumped 1.7 units to 8.9. Not great as 10 is regarded as the danger level. However the GP I was seeing said I had to get a biopsy done as soon as possible as a jump of 1.7 units in six months was not good. I sort of demurred but decided to use Bayes theorem to work out the probability that I had prostate cancer?

The chances of having prosetate cancer at various ages are as follows:

For a man in his 40s - 1 in 1000

For a man in his 50s - 12 in 1000

For a man in his 60s - 45 in 1000

For a man in his 70s - 80 in 1000

I am 69 so my chances of prostate cancer would be 63 in 1000. However I have now had a positive PSA test result.

Now according to a medical website for every 100 men over age 50, with no symptoms, who have the PSA test:

10 men out of 100 tested will have a higher than normal level of PSA. These men must then go through other tests and examinations. At the end of these tests:

• Three of the ten men with a higher than normal PSA level will be found to have prostate cancer.