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BGonline.org Forums
Probability Problem
Posted By: Bob Koca In Response To: Probability Problem (Gregg Cattanach)
Date: Thursday, 27 August 2009, at 4:19 p.m.
The problems P(both are aces GIVEN that at least one is an ace) and P(both are aces GIVEN that one is the ace of Spades) both have clear answers and answers to those have been given correctly. However, the information was told to you by that lady. Perhaps she is more likely to say "at least one is an ace" if they actually both are. Without any idea on what spurs to say such a thing the problem is is intractable. Now if she had instructions beforehand of "I will deal you two cards, you will look at both and then answer yes or no the question, "is at leat one of the cards an ace"" then it is amenable to the reduced sample space analysis.
Here is a more extreme example to show this idea. A wife purchases a sweepstakes entry (by putting her name on it). there were 10,000 entrees sold. The morning of the drawing the husband reasonably thnks P(she wins) = .00001 The drawing is at 6pm and at 6:01 pm he getsw a text from his wife. Someone won the loteery guess who!. Would he still say .00001 as the probability. Even an "absence" of information can be information. Suppose he in a remote place with outside communication. If the drawing was at 6pm he could still at 7pm be thinking "There is a .00001 probasbility that she won. But if he is communication and has not heard anything by 7pm it is reasonable to lower that value.
Hmm. Kind of goes against Stick's exhortation to make the analysis simpler. LOL
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