A store sells three brands of cigarettes: $3.15 Star lights, $4.30 Vegas slims, and $5.20 Royal 100's. (Tax included) A man named Smokey walks into the store, and buys 2 packs of cigarettes, one pack for himself and the other pack for a friend. He hands the cashier a $20 note, and is returned a few bills and 3 coins in change (exclude dollars or half dollars). What's the probability, that the man smokes Royal 100's?
I suppose Charlie has the best case, BUT...
Of the nine possible purchase scenarios, only four (Smokey first in each case) would present the three-coin return: (3.15 + 4.30 QQN), (4:30 + 3.15 QQN), (4:30 + 4.30 QDN), (5.20 + 5.20 QQD). BUT are each of THOSE FOUR really EQUALLY likely? Would Smokey be equally likely to buy two Royals if that were not also the brand of one of his pals? He could also have bought two Vegas, if that was his brand. The other two cases arise when Smokey and a friend smoked Star and Vegas respectively. Perhaps the most likely is that he buy two Vegas OR two Royal -- in which case the odds are 1/2 for Royals.
If the change received showed no combination of a Royal with any second purchase, clearly that would give him a zero probability; perhaps otherwise we are stuck with the antecedent probability (1/3) as the best we could guess.
And, then again perhaps Smokey does not smoke at all (perhaps buys a pack "for himself" to be sociable, or whatever... Probably almost any suggested probability could be given some support from the paucity of data. Only John can tell us if he is playing a joke on us all.