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Metalworking (rec.crafts.metalworking) Discuss various aspects of working with metal, such as machining, welding, metal joining, screwing, casting, hardening/tempering, blacksmithing/forging, spinning and hammer work, sheet metal work. |
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Very OT - probability paradox
Given: an opaque jar with a large number of white & black marbles, same
number of each. If I pick 2 marbles randomly, it seems that the probabilities depend upon how I do the drawing. If I pick one marble, then pick another, the probability of drawing one black and one white marble is 50%. (4 possibilities, 2 of which give 1 white & 1 black.) If I reach in and pick 2 marbles AT ONCE, the probability is 33%. (3 possibilities, 1 of which gives 1 of each color.) It just doesn't SEEM right that the probabilities could be different. Why is it different? Or is it not different? Is there really 4 possibilities when drawing 2-at-once? Drawing 3 marbles gives even worse results. One-at-a-time gives: 1/8 probability of all black, 1/8 all white, 3/8 2 black + 1 white, & 3/8 2 white + 1 black. 3 at once gives: 1/4 all black, 1/4 all white, 1/4 2 black + 1 white, & 1/4 2 white + 1 black. The probability of drawing all same color 3-at-once is twice that of one-at-a-time! Is there a statistician in the house? Bob |
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