1% chance of guilt has risen to almost 9%. If the prosecution had made the
greater claim that the probability of finding the incriminating weapon was as high
as 0.99 if the prisoner is guilty but if innocent the probability of finding the
weapon was only 0.01, then repeating the Bayes’s formula calculation the juror
would have to revise their opinion from 1% to 50%.
Using Bayes’s formula in such situations has been exposed to criticisms. The
leading thrust has been on how one arrives at the prior probability. In its favour
Bayesian analysis presents a way of dealing with subjective probabilities and how
they may be updated based on evidence. The Bayesian method has applications
in areas as diverse as science, weather forecasting and criminal justice. Its
proponents argue its soundness and pragmatic character in dealing with
uncertainty. It has a lot going for it.

the condensed idea

Updating beliefs using evidence