Word nerds: This challenge of homophones and syllables is for you.
you to a probability puzzle from the mind that brought us the Mad Hatter. Many people have a strong intuition that there is a 1/2 chance that the marble remaining in the bag is white. There was a 1/2 chance at the beginning, and your gut might tell you that tossing in a white marble and then picking a white marble out of the bag should not change this likelihood. This instinct turns out to be wrong. The actual probability that a white marble remains is 2/3.
We don’t know which of these two bags we’re holding. When we observe that we picked a white marble from the bag, there areWe’re holding bag A and picked the New White Marbleremaining marble in the bag is white . This is how we conclude that there is a 2/3 chance that the remaining marble is white. Intuitively, what’s happening here is that we’re more likely to pick a white marble from the bag if we’re holding bag A. The flip side of this is that when we pick a white marble, it serves asthat we’re more likely to be holding bag A than bag B.
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