tag:blogger.com,1999:blog-15628310.post6995538906818442163..comments2021-03-02T05:02:26.838-05:00Comments on Question of the day: Three Darts in One HemisphereAnonymoushttp://www.blogger.com/profile/18153935609499338685noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-15628310.post-87854712834156428742011-09-27T08:29:49.375-04:002011-09-27T08:29:49.375-04:00Aidan and Anonymous have it right. The probabilit...Aidan and Anonymous have it right. The probability is 1 that all three darts are in one hemisphere.<br /><br />For a longer explanation than what Aidan gives, you can check out this elementary probability book: http://portal.tpu.ru/SHARED/k/KITAEVA/statistics/book/Tab2/ElementaryProbabilityDavidStirzaker.pdf<br />Just search through the document for the keyword sphere. Then you'll have to read over the chapter.<br /><br />Warning, it's not that elementary to figure out the math!Anonymoushttps://www.blogger.com/profile/18153935609499338685noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-40104187827148172322011-09-20T22:29:30.343-04:002011-09-20T22:29:30.343-04:00Confused? What is the answer?Confused? What is the answer?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15628310.post-25608549761532009372011-09-20T12:04:59.154-04:002011-09-20T12:04:59.154-04:00The probability is 1. You can draw a circle throug...The probability is 1. You can draw a circle through any three points in space, and since any section of a sphere leaves a circular cut the circle through three darts must lie on the surface of the sphere. Since this circle could not be bigger than a great circle, they must lie in a single hemisphere.Aidannoreply@blogger.comtag:blogger.com,1999:blog-15628310.post-41939262420492477792011-09-19T14:56:23.770-04:002011-09-19T14:56:23.770-04:001/3?1/3?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15628310.post-42458778072700033182011-09-17T11:38:47.508-04:002011-09-17T11:38:47.508-04:00100% on the upper hemisphere100% on the upper hemisphereAnonymousnoreply@blogger.com