tag:blogger.com,1999:blog-15628310.post5454184377033232840..comments2021-03-02T05:02:26.838-05:00Comments on Question of the day: I am Feeling a Little Bit Probabilistic TodayAnonymoushttp://www.blogger.com/profile/18153935609499338685noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-15628310.post-52281502657317984412010-03-17T08:47:23.252-04:002010-03-17T08:47:23.252-04:00Nice work Andy. I came at it a little bit differe...Nice work Andy. I came at it a little bit differently, but came up with the same answer.<br /><br /><br />Select any blue marble, then arrange the 11 remaining marbles in a line. That's the same as putting them into a ring.<br /><br />The number of ways to choose k out of n is (N choose k) n!/(k!(n-k)!)<br /><br />Choosing 4 red marbles out of 11 is 330.<br /><br />I basically did the same as you, Andy, and counted up the number of ways to divide up the marbles, and came up with 70 distinct combinations (8 choose 4).<br /><br />Therefore the probability that no two red marbles are adjacent is 70/330 = 7/33.Anonymoushttps://www.blogger.com/profile/18153935609499338685noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-16192032429858514522010-03-16T13:36:02.756-04:002010-03-16T13:36:02.756-04:00I came up with 7/33 ~ 21.2%
The total number of p...I came up with 7/33 ~ 21.2%<br /><br />The total number of possible ball combinations where 4 are red and 8 are blue is:<br />12!/(8! * 4!) = 495<br /><br />The number of combinations where red doesn't repeat is 105. <br /><br />I'm sure there's a formula for this, but I just counted out each scenario. For example, if marble 1 is red, there are 35 ways to have 3 more red marbles that aren't consecutive. The same is true for marble 2 being red. Then for marble 3 being red, there are 20 ways without having consecutive red marbles or a red marble 1. Etc...you eventually end up with:<br /><br />35+35+20+10+4+1=105<br /><br />So that makes the probability that no two red marbles are adjacent:<br /><br />105/495 = 7/33Andyhttps://www.blogger.com/profile/14117563810484999900noreply@blogger.com