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Old 13th November 2012, 06:24 AM   #4073
Jabba
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Carbon Dating/Smoking Gun?/Probability

Originally Posted by Humots View Post
Because as I understand it, the question is not:

What is the probability that we select the All-Ace deck and draw an Ace?
vs
What is the probability that we select the regular deck and draw an Ace?

It is:

If we draw a card from a deck (and we don't know which one) and the card is an Ace, what is the probability that we drew from the All-Ace deck?

The point is, there are not two separate events, each with its own probability. There is only one event: drawing a card from a deck and the card is an ace.
Humots,
- Unfortunately, I don't follow the reasoning.
- Agreed that there is only one event in our little scenario, but there are two ways that event could have happened -- either you drew from the Ace deck or you drew from the normal deck.
- If the overall probability of first selecting the ace deck and then drawing an ace from it is 2%, and the overall probability of first selecting the normal deck and then drawing an ace from it is almost 8%, why can't we conclude that the 2nd way is almost 4 times as likely to be the way it actually happened?
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