Black and white marbles probability question

  • #1
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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

  • #2
Dale
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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.
 
  • #3
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I mean selecting one marble and it being black...
 
  • #4
phinds
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Pretty trivial to just jot down the very small number of possible situations and it will be obvious what the answer is.
 
  • #6
974
47
Yes, understood
OK, thanks, been suspecting the "must" in that statement was too exclusive.
 

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