Bayesian revision of probabilities
Seepage from dams containing uranium tailings is known to cause radio-active pollution of surrounding ground water of an average of 1 dam in 2000. The presence of radio-active pollution can be tested using a geiger-counter. This instrument, however, provides imperfect signals. Background atmospheric radiation causes it to indicate the presence of radio-active seepage on 15% of the occasions when no radio-active seepage has occurred. However, when radio-active seepage has occurred, it fails to accurately signal the presence of radio-active pollution only 2% of the time.
If a geiger-counter measurement indicates the presence of radio-active pollution, what is the probability that radio-active seepage has occurred?