tag:blogger.com,1999:blog-264226589944705290.post1272877877769668562..comments2024-09-25T08:51:01.854-07:00Comments on God Plays Dice: In which I declare four things which my probability class is not aboutMichael Lugohttp://www.blogger.com/profile/15671307315028242949noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-264226589944705290.post-72071813375106418232011-11-17T06:04:47.167-08:002011-11-17T06:04:47.167-08:00And, of course, being an idiot, I could not see th...And, of course, being an idiot, I could not see that this is a geometric with parameter 0.5*p :-)Panos Ipeirotishttps://www.blogger.com/profile/15283752183704062501noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-69996497836105592362011-11-17T05:59:02.906-08:002011-11-17T05:59:02.906-08:00Assume t is the total number of children, and b is...Assume t is the total number of children, and b is the number of boys.<br /><br />Pr(t) = p^t*(1-p)<br /><br />Since we have equal probability of boys and girls, if we know the total number of children t:<br /><br />Pr(b|t) = binomial(t,b) * 0.5^b * 0.5^(t-b)<br /><br />Now, we want the number of children, given the number of boys:<br /><br />Pr(t|b) = Pr(b|t) * Pr(t) / Pr(b)<br /><br />= binomial(t,b) * 0.5^t * p^t*(1-p) / sum)t (Pr(b|t) *P(t)<br /><br />For b=0, we have (1-p/2)*p^t*0.5^t<br /><br />I have no idea what is the name of this distribution though :-)Panos Ipeirotishttps://www.blogger.com/profile/15283752183704062501noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-83646397876319109742011-11-16T18:21:43.900-08:002011-11-16T18:21:43.900-08:00Let the number of homes with one child be 2x, then...Let the number of homes with one child be 2x, then half would have no boys. If the family has two children, then the probability of having no boys would be (1/2)ˆ2; with three children, the probability would be (1/2)ˆ3 etc.<br /><br />The distribution would be a function Y, being equal to 2x*(1/2)^n. And n could assume values from 1 to infinity. In the case of n=1, the number of families with no boy would be x.Rafaelhttps://www.blogger.com/profile/13003288905996590360noreply@blogger.com