Originally Posted by
Jabba
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?
--- Jabba
In your link, you state (bolding mine):
Quote:
So, once you draw the ace, to determine what the probability is that you drew from the ace
deck, you need to compare the two composite probabilities, and ultimately you end up being about 4 times as likely -- .075385/.02 -- to have drawn from the normal deck…
This is wrong. The event is not "drawing from the Ace deck or the normal deck". It is drawing an ace, and there are two possible ways to do this: "from the Ace deck or from the normal deck".
The question is, what is the probability that an ace, once drawn, came from the Ace deck?
One composite probability value is about four times the other, but that does not mean the probability of drawing from the ace deck once an ace has been drawn is as you state.
Determining this probability is a bit more complicated than simply comparing one composite probability against the other.
I'm not a math teacher (nor do I play one on TV) so I can't come up with my own argument in a reasonable time.
So please take a look at the Wiki entry on Bayes' Theorem. I can't give a direct URL (too few posts), but you can copy and paste
en.wikipedia.org/wiki/Bayes_theorem
into your browser.
See the Introductory Example for a scenario similar to yours.