Editing 1374: Urn
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
| Latest revision | Your text | ||
| Line 14: | Line 14: | ||
[[Megan]], when asked to imagine drawing balls from an urn, imagines a cremation urn containing not only balls, but also human remains. She may be referring to a real grandfather who has been cremated, or is simply improvising a joke at Cueball's expense. | [[Megan]], when asked to imagine drawing balls from an urn, imagines a cremation urn containing not only balls, but also human remains. She may be referring to a real grandfather who has been cremated, or is simply improvising a joke at Cueball's expense. | ||
| β | The title text refers to two distinct scenarios in the | + | 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. She might also want to have her grandfather back, and be playing with the word "replacement". |
| β | 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 | + | 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 {{w|binomial distribution}}, but if the balls are not replaced, so that the same ball cannot be drawn twice, you instead get the {{w|hypergeometric distribution}}. |
There are a myriad of reasons why Megan would want to draw with replacement, the most simple of which being that she has nowhere to put ashes other than in their designated urn. Ashes by their nature need a container, or they will make a mess; cremated remains in particular come with the additional requirement that the container be respectful to the deceased. | There are a myriad of reasons why Megan would want to draw with replacement, the most simple of which being that she has nowhere to put ashes other than in their designated urn. Ashes by their nature need a container, or they will make a mess; cremated remains in particular come with the additional requirement that the container be respectful to the deceased. | ||
