# Black and white marbles probability question

## 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...
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).

## Answers and Replies

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Dale
Mentor
2020 Award
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.

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

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

Dale
Mentor
2020 Award
I mean selecting one marble and it being black...
Yes, understood

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