tag:blogger.com,1999:blog-3802979373213475425.post7374466736548767043..comments2017-05-26T15:18:48.592+05:30Comments on Critical Thinking Puzzles: Birth ProbabilityEldhose Babyhttps://plus.google.com/111638910038568381260noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-3802979373213475425.post-19684533631446580252014-11-12T13:18:24.637+05:302014-11-12T13:18:24.637+05:30How does one get to know the correct answer? Will ...How does one get to know the correct answer? Will the author post the correct answer?arushinoreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-71194862614771485812014-11-12T13:11:29.010+05:302014-11-12T13:11:29.010+05:30Thus, proportion = no of boys/no of girls
= n/n =...Thus, proportion = no of boys/no of girls<br /> = n/n =1arushinoreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-45503404115626424582014-11-12T13:10:16.298+05:302014-11-12T13:10:16.298+05:30Thus, expected no of girls born = mean of negative...Thus, expected no of girls born = mean of negative binomial distribution<br />= nq/p = n (since p=q=1/2)<br /> arushinoreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-85791573557261638972014-11-12T13:07:53.154+05:302014-11-12T13:07:53.154+05:30Considering all n families, the total no of girls ...Considering all n families, the total no of girls born before n boys (is total no of failures before nth success) follows negative binomial distribution with parameters (n, 1/2)arushinoreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-91642852904587841022014-11-12T13:03:33.143+05:302014-11-12T13:03:33.143+05:30If there are n families, the total no of boys born...If there are n families, the total no of boys born is n because births take place until a boy is born in each family.arushinoreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-15424900325016415472014-11-12T12:02:10.971+05:302014-11-12T12:02:10.971+05:30Answer is 1.
Girls Boys Probability
0 1 0.5
1 1 0...Answer is 1.<br /><br />Girls Boys Probability<br />0 1 0.5<br />1 1 0.25<br />2 1 0.125<br />3 1 0.0625<br />4 1 0.03125<br />5 1 0.015625<br />6 1 0.0078125<br />7 1 0.00390625<br />8 1 0.001953125<br />9 1 0.000976563<br />10 1 0.000488281<br />11 1 0.000244141<br />12 1 0.00012207<br />13 1 6.10352E-05<br />14 1 3.05176E-05<br /><br />Though the number of girls seems to be increasing, the likelihood of that event is getting lower.<br /><br />With 50% chances a couple will have only a boy. And for the rest 50% chances atleast one girl. If you calculate #girls*probability and sum it up, it comes out to be 1 and similarly #boys*probablity and sum it up, it comes out to be 1 (both are an Infinite series with sum 1). Thus the proportion is 1.<br /><br />Intuitively, Population proportion will be male biased only if events like female foeticide, etc. starts happening (Where chances of having a boy are forcefully increased, eg. Some states in India). Else the likelihood is to have a balanced mix of population.<br /><br />Desiring a male child doesn't seems to be a problem but female foeticide is.Raghavhttp://www.blogger.com/profile/09186521256836841332noreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-8128080845851545122014-11-12T01:20:45.863+05:302014-11-12T01:20:45.863+05:30Since the families keep having children until they...Since the families keep having children until they have a boy, the possible outcomes are:<br /><br />Girls Boys<br /> 0 1<br /> 1 1<br /> 2 1<br /> 3 1<br /> 4 1<br /> 5 1<br /> 6 1<br /> 7 1<br /> 8 1<br /> 9 1<br /> 10 1<br /><br />Etc.<br /><br />The number of girls is the sum of an arithmetic series (n/2)*(2+(n-1)). The number of boys is n+1.<br /><br />Since both sums are unbounded, the probability is determined by the maximum number of children (assum)ng an equal distribution of all outcomes - which in itself is not likely).<br /><br />Anyways for n = 10 (ie. up to eleven children, Prob is 1/5.Larrynoreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-45920693069833316392014-11-11T23:31:26.922+05:302014-11-11T23:31:26.922+05:30probability versus actual statistics does not prod...probability versus actual statistics does not produce a definitive answer. So a guess is the best answer. Long winded explanation of "I don't know"!Ron McCuenhttp://www.blogger.com/profile/16707162375539924351noreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-66584068715201237662014-11-11T23:10:14.492+05:302014-11-11T23:10:14.492+05:30One to oneOne to oneRamnoreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-20006361293020772632014-11-11T20:27:45.579+05:302014-11-11T20:27:45.579+05:30Don't know but I want to live there.Don't know but I want to live there.MarkDrunoreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-46167127383673523232014-11-11T18:40:10.544+05:302014-11-11T18:40:10.544+05:302 girls to one boy.2 girls to one boy.Anonymousnoreply@blogger.com