This is essentially a textbook example from Chapter 5 of Probability Theory: The Logic of Science http://www.med.mcgill.ca/epidemiology/hanley/bios601/Gaussia

This is essentially a textbook example from Chapter 5 of Probability Theory: The Logic of Science http://www.med.mcgill.ca/epidemiology/hanley/bios601/GaussianModel/JaynesProbabilityTheory.pdf http://www.med.mcgill.ca/epidemiology/hanley/bios601/Gaussia... "...The new information D is: ‘Mr. N has gone on TV with a sensational claim that a commonly used drug is unsafe’, and three viewers, Mr. A, Mr. B, and Mr. C, see this. Their prior probabilities P(S|I) that the drug is safe are (0.9, 0.1, 0.9), respectively; i.e. initially, Mr. A and Mr. C were believers in the safety of the drug, Mr. B a disbeliever. But they interpret the information D very differently, because they have different views about the reliability of Mr. N. They all agree that, if the drug had really been proved unsafe, Mr. N would be right there shouting it: that is, their probabilities P(D|SI) are (1, 1, 1); but Mr. A trusts his honesty while Mr. C does not. Their probabilities P(D|SI) that, if the drug is safe, Mr. N would say that it is unsafe, are (0.01, 0.3, 0.99), respectively. ... Put verbally, they have reasoned as follows: A) - Mr. N is a fine fellow, doing a notable public service. I had thought the drug to be safe from other evidence, but he would not knowingly misrepresent the facts; therefore hearing his report leads me to change my mind and think that the drug is unsafe after all. My belief in safety is lowered by 20.0 db, so I will not buy any more. B) - Mr. N is an erratic fellow, inclined to accept adverse evidence too quickly. I was already convinced that the drug is unsafe; but even if it is safe he might be carried away into saying otherwise. So,hearing his claim does strengthen my opinion, but only by 5.3 db. I would never under any circumstances use the drug. C) - Mr. N is an unscrupulous rascal, who does everything in his power to stir up trouble by sensational publicity. The drug is probably safe, but he would almost certainly claim it is unsafe whatever the facts. So hearing his claim has practically no effect (only 0.005 db) on my confidence that the drug is safe. I will continue to buy it and use it."