tag:blogger.com,1999:blog-8231784566931768362.post2413975568927012657..comments2023-09-09T08:21:55.454-04:00Comments on MathNotations: Please Help Dorothy Go Home - A Probability Fantasy for Middle School and BeyondDave Marainhttp://www.blogger.com/profile/13321770881353644307noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-8231784566931768362.post-69011421605686799112009-07-11T18:06:34.802-04:002009-07-11T18:06:34.802-04:00I left a comment, but I think blogger ate it.
Let...I left a comment, but I think blogger ate it.<br /><br />Let's modify things a bit. Have the kid keep drawing cards, even after they win. Won't change the probability, they've already won. But it simplifies the game. Now each play consists of drawing all but one card.<br /><br />The modified game is equivalent to the original game. This modification may be difficult to explain, but now the math is accessible to much younger children.<br /><br />JonathanAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-23467931667309101352009-06-26T18:30:14.309-04:002009-06-26T18:30:14.309-04:00I think some of them could figure out the general ...I think some of them could figure out the general formula, but most could probably not justify it.mathmomhttps://www.blogger.com/profile/05869925405540832241noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-19793282199802956202009-06-26T17:47:01.657-04:002009-06-26T17:47:01.657-04:00I would count those as 2 different methods.
Yes, ...I would count those as 2 different methods. <br />Yes, the general case may be beyond them but working with a few special cases like 3, 4 and 5 might lead to a simple generalization. The general formula for losing is 1/n and the simplicity of that result suggests there might be a clever approach.Dave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-29189851329377642882009-06-26T17:00:29.763-04:002009-06-26T17:00:29.763-04:00Nice, but beyond most middle-schoolers I believe (...Nice, but beyond most middle-schoolers I believe (at least the general case).<br /><br />Does computing the probability of winning, and computing the probability of losing and subtracting from 1 count as 2 separate methods? <br /><br />For the simple case students might try to just enumerate the possible outcomes, but it's a bit of a leap to prove that they're all equally likely.mathmomhttps://www.blogger.com/profile/05869925405540832241noreply@blogger.com