There are two parcels, one marked CALCUTTA and one marked TATANAGAR which get lost in transit. One parcel is found and has the label partly torn (the label can be torn in any manner). It only has the letters 'TA' (adjacent letters). What is the probability that the recovered parcel was marked CALCUTTA?

(In reply to Posterior thinking (spoiler?) by Steve Herman)

I appreciate that 4/11, 7/11 is supposed to be the 'canonical' answer, but I still just don't see it. The alternative ways into which the tags might have been, but had not in fact been, torn, as at the time of observation seem to me to remain firmly in the realm of hypothetical abstraction.  What is relevant about the original labels is that there are two "histories' in which TATANAGAR could have been torn leaving the 'given' of the problem, i.e the observed TA, and one 'history' for CALCUTTA, so all other things being equal, the probability ought to be 2/3, 1/3.

I'd love to see someone do a simulation of this together with some other 'control' destination like TARTARSTAN to see whether the probabilities actually do stack up in a Bayesian manner or not!

 

Posted by broll on 2010-10-28 16:35:26