fyjham wrote:*snip*Fixed your tree for you.

Code: Select all

P

/ | \

/ | \

B M W

/ \ / \ / \

B B B W W W

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B B W B W W

If you're going to tally up the nodes at the bottom as your proof make sure the probability at each split is identical (you have 1 branch for a 100% on the B/B and the W/W, with 1 branch for a 50% on the mixed one

No, I had it correct, I intended to show that when you select either the white/black pancake you'ld get the same colour. My explanation why was terrible, let me try to explain in better.

When you have Pr(x|y) it means y is a certain event, even if I had y happening as 1 against 1000 it would still happen. We know in this problem that showing the black side is a certain event. What this means is that on the event Pr(first side black) is equal to 1 (certain). What you want to do then is find out from here is Pr(2nd side black).

If we select the black pancake if the first side is black then the 2nd side is black at a 100% chance.

If we select the mixed pancake if the first side is black then the 2nd side is black at a 0% chance.

If we select the white pancake we realize this event cannot have occured as a black side must have been chosen.

Now we have a 50% chance of chosing the black pancake, and a 50% chance of chosing the mixed pancake given that we know the 1st side is black.

Pr(2nd side black|1st side black) = Pr(black pancake AND 2nd side black | 1st side black) + Pr(mixed pancake AND 2nd side black | 1st side black)

Pr(2nd side black|1st side black) = Pr(black pancake | 1st side black)*Pr(2nd side black | black pancake AND 1st side black) + Pr(mixed pancake | 1st side black)*Pr(2nd side black | mixed pancake AND 1st side black)

We fill in the probabilities for the above

Pr(black pancake | 1st side black) = 0.5

Pr(mixed pancake | 1st side black) = 0.5

Pr(2nd side black | black pancake AND 1st side black) = 1

Pr(2nd side black | mixed pancake AND 1st side black) = 0

Pr(2nd side black|1st side black) = 0.5*1 + 0.5*0

Pr(2nd side black|1st side black) = 0.5

Thats a 50% chance.

I may not have explained this thouroughly enough, but I hope it shows you how I came to the answer of 50% chance, which I belive is mathematically correct. If someone can find an error with the proof that I've provided then I'll be happy to hear it.