Quote:
Originally Posted by BruceZ
If A draws from another distribution it doesn't matter what he draws. Or are you saying that he is putting that ball into the urn before C draws? In that case it would be different as above.
Sorry, I might be confusing you with my choice of words. When I am saying that A draws from a different distribution, I mean that A has a different probability of drawing a red ball. Let me try again:
We have two people, A and C. On a table we have an urn with 25 white balls and 5 red balls. A draws 1 (without replacement!) and
after that C draws one. We want to find the probability that C draws a red ball.
Setting 1:
P(A draws red) = #red/#total.
P(C draws red) = #red/#total.
P(C draw 1 red and draws first) = 5/30.
P(C draw 1 red | A draws first) = P(C draw 1 red | A draws 0 red)*P(A draws 0 red) + P(C draw 1 red | A draws 1 red)*P(A draws 1 red)
=(5/29)*(25/30) + (4/29)*(5/30) = 5/30.
Setting 2:
Say A knows that the right side of the urn contains more red balls than the left. A decides to draw from the right side (changing his chances of getting a red ball).
P(A draws red) = 2*#red/#total.
P(C draws red) = #red/#total.
P(C draw 1 red and draws first) = 5/30.
P(C draw 1 red | A draws first) = P(C draw 1 red | A draws 0 red)*P(A draws 0 red) + P(C draw 1 red | A draws 1 red)*P(A draws 1 red)
=(5/29)*(20/30) + (4/29)*(10/30) = 14/87.
We see that in Setting 1 we have:
P(C draw 1 red | A draws first) = P(C draw 1 red and draws first)
And in setting 2 we have
P(C draw 1 red | A draws first)
!= P(C draw 1 red and draws first)
and my question becomes why this is? It seems that (and I am convincing myself of that this is the right thought process now) the thing that makes us able to not consider A's draw in Setting 1 is, that she draws "from the same distribution" (i.e. with the same probability) as C. Is this correct?
In your poker example of getting dealt aces it would translate to: You are equally likely of getting dealt aces in the SB and on the button. But if for some reason MP is twice as likely to get dealt an ace than the rest of you, this obviously is not the case any more.