Posted: Jul 06, 2012 11:43 pm
Daniel Kahneman is correct. Each of the three sequences is equally likely.
However, if you grouped all the possible sequences into kinds of sequence, then some kinds of sequence would be more likely than others, because different kinds of sequences will correspond to different numbers of individual sequences.
e.g. How likely is it that all the children have the same gender (all B or all G)? There are only two individual sequences for which this is the case: BBBBBB and GGGGGG. On the other other hand, there are many more individual sequences for which it is not the case, so we can say that "all the same gender" is unlikely - but it would still be wrong to say that some particular sequence of the "all the same gender" kind (e.g. GGGGGG) is less likely than some particular sequence of the "not all the same gender" kind - which is the fallacy which he is discussing.
However, if you grouped all the possible sequences into kinds of sequence, then some kinds of sequence would be more likely than others, because different kinds of sequences will correspond to different numbers of individual sequences.
e.g. How likely is it that all the children have the same gender (all B or all G)? There are only two individual sequences for which this is the case: BBBBBB and GGGGGG. On the other other hand, there are many more individual sequences for which it is not the case, so we can say that "all the same gender" is unlikely - but it would still be wrong to say that some particular sequence of the "all the same gender" kind (e.g. GGGGGG) is less likely than some particular sequence of the "not all the same gender" kind - which is the fallacy which he is discussing.