- #1

- 974

- 47

## 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).

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).