Suzie’s suspicion is correct. According to Bayes’s theorem, the probability that he pulled it out randomly would be .05 x prior probability that he would pull out a marble randomly / prior probability that he would be found holding the red marble.
In this case it is rather difficult to calculate an exact number. But in Eliezer’s case, an exact number is unnecessary; the ”.05″ in his case is so low that he assumes that the exact number will also be low, regardless of the particular values assigned to “prior probability of pulling out a marble randomly” and “prior probability that he ends up with a red marble.”
Suzie’s suspicion is correct. According to Bayes’s theorem, the probability that he pulled it out randomly would be .05 x prior probability that he would pull out a marble randomly / prior probability that he would be found holding the red marble.
In this case it is rather difficult to calculate an exact number. But in Eliezer’s case, an exact number is unnecessary; the ”.05″ in his case is so low that he assumes that the exact number will also be low, regardless of the particular values assigned to “prior probability of pulling out a marble randomly” and “prior probability that he ends up with a red marble.”