Editing 1374: Urn
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==Explanation== | ==Explanation== | ||
− | A common | + | {{incomplete|More in-depth? Why does Megan imagine that the urn contains ashes?}} |
+ | A common scenario for teaching elementary probability theory is drawing coloured balls from a container, such as a bag, hat, and traditionally quite often an urn. The word 'urn' is by many people (apparently including Megan) associated with the receptacle used to collect the human (or possibly animal) ashes that remain after a cremation. This explains why Megan, when asked to imagine drawing balls from an urn, imagines an urn containing not (only) balls, but (also) human remains. One could speculate that her grandfather recently died, leading her to make this irrational connection. | ||
− | + | The title text refers to two distinct scenarios in the coloured ball experiment: The balls may be replaced between each drawing, or not. In the former case, each draw is independent of the previous, in the latter the chances of picking a particular (remaining) ball the next time have increased. Megan (or rather Randall if it is he who speaks in the title text) would prefer to put the ashes back into the urn. | |
− | + | The distinction between repeated drawing with and without replacement is used in most presentations of elementary probability because it illustrates a subtle but important theoretical distinction: if the balls are replaced, one at a time, before drawing the next, the number of balls of a certain colour has the [http://en.wikipedia.org/wiki/Binomial_distribution binomial distribution], but if the balls are not replaced, so that the same ball cannot be drawn twice, you instead get the [http://en.wikipedia.org/wiki/Hypergeometric_distribution hypergeometric distribution]. | |
− | + | ==Transcript== | |
+ | [Cueball is standing in a classroom with Megan at a desk.] | ||
− | + | Cueball: Imagine that you're drawing at random from an urn containing fifteen balls - six red and nine black. | |
− | + | Megan: OK. I reach in and... '''''My grandfather's ashes?!? Oh god!''''' | |
− | + | Cueball: I... what? | |
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− | : | + | Megan: '''''Why would you do this to me?!?''''' |
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{{comic discussion}} | {{comic discussion}} | ||
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