Black and white marbles probability question

[bahamagreen]

TL;DR

Bag with two marbles, each p=.5 of being black or white. After adding a third black marble, what is p of selecting a black marble from the bag? I get 2/3 which impossibly reveals the two marbles' colors. Not finding the flaw...

Two-marble probabilities
BB 1/4
BW 1/2
WW 1/4

Three-marble probabilities of selecting a black
B BB 1
B BW 2/3
B WW 1/3

Probability of selecting a black marble if we add a black marble to the two marble bag
(1 x 1/4) + (2/3 x 1/2) + (1/3 x 1/4) = 2/3

Three marbles with 2/3 probability of selecting black must mean two black and one white. If I remove (mentally) the black marble I added, I impossibly "know" the colors of the initial randomly selected two-marble bag (although I'm only right half the time).

 

[Dale]

Summary:: Bag with two marbles, each p=.5 of being black or white. After adding a third black marble, what is p of selecting a black marble from the bag? I get 2/3 which impossibly reveals the two marbles' colors. Not finding the flaw...

Three marbles with 2/3 probability of selecting black must mean two black and one white.

This is not correct. 2/3 probability of selecting black could also mean a 1/4 probability of one black and two white plus a 1/2 probability two black and one white plus a 1/4 probability of three black.

 

[bahamagreen]

I mean selecting one marble and it being black...

 

[phinds]

Pretty trivial to just jot down the very small number of possible situations and it will be obvious what the answer is.

 

[Dale]

I mean selecting one marble and it being black...

Yes, understood

 

[bahamagreen]

Yes, understood

OK, thanks, been suspecting the "must" in that statement was too exclusive.