Dan_Nelson

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But There's Still A Chance, Right?

Let's say you and your friend Suzie bumped into a guy on the street. This guy is holding a red marble in his right hand, and a velvet bag in his left. You and Suzie ask the man what is in the velvet bag. You realize very quickly that he doesn't speak your language. You take the velvet bag to see for yourself what is inside. It contains 19 blue marbles. In fact, it has a sticker on the outside of the bag that says "Contents: 1 red marble, 19 blue marbles". Suzie wonders out loud whether the man looked in the bag and specifically pulled out the red marble or simply pulled out a random marble without looking and it just so happened to be the red marble. Suzie is very, very attractive, by the way.

"Well," you respond to her wonderings, "the chances someone would pull out the red marble if they weren't looking are 1 in 20."

Suzie looks at you, "Hmmm. Well, yes, that is indeed the probability of randomly pulling out the single red marble from a bag of 20 marbles. But I'm not sure that's the probability we are looking for in this situation. Our situation is that the man is actually holding the red marble. Something tells me the probability the man did in fact pull the red marble out randomly, given the fact that the man is holding the red marble, is different than the before-the-action probability that he would pull the red marble randomly from the bag."

Is Suzie's suspicion correct? I would really like to hear Eliezer's answer to this.