A rare symptom S is a possible effect of three diseases: A, B and C. The symptom never occurs in people who do not have one of the three diseases. The diseases are rare and it never happens that someone has more than one of the diseases.

The frequency of disease A in the population is 3 in 100000; the frequency of disease B in the population is 5 in 100000 and the frequency of disease C in the population is 7 in 100000.

If you have disease A, your chance of developing symptom S is 1/3. If you have disease B, your chance of developing the symptom is 1/4 and if you have disease C your chance of developing the symptom is 1/10.

If you develop the symptom, find are your chances that you have diseases A, B and C respectively.