Some teasers concerning conditional probabilities


Authors: 
Bar-Hillel, M., & Falk, R.
Category: 
Volume: 
11
Pages: 
109-122
Year: 
1982
Publisher: 
Cognition
Abstract: 

A family of notorious teasers in probability is discussed. All ask for the probability that the objects of a certain pair both have some property when information exists that at least one of them does. These problems should be solved using conditional probabilities, but cause difficulties in characterizing the conditioning event appropriately. In particular, they highlight the importance of determining the way information is being obtained. A probability space for modeling verbal problems should allow for the representation of the given outcome and the statistical experiment which yielded it. The paper gives some psychological reasons for the tricky nature of these problems, and some practical tips for handling them.

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