Author: Serge Desmarais
Date: 16:21:48 08/29/98
Go up one level in this thread
On August 29, 1998 at 17:33:54, Dan Newman wrote: >On August 29, 1998 at 07:14:10, Serge Desmarais wrote: > >>On August 29, 1998 at 05:39:43, Dan Newman wrote: >> >>>On August 28, 1998 at 23:30:44, Serge Desmarais wrote: >>> >>>>On August 18, 1998 at 07:26:14, fca wrote: >>>>>A man has exactly two biological children. >>>>>Question (1): "One of them is a B. What is the probability that both are Bs?" >>>>>Question (2): "The older of them is a B. What is the probability that both are >>>>>Bs?" >>>>> >>>>>Now the answer to (1) is 1/3, and to (2) is 1/2. >>>> >>>> >>>> >>>> I don't understand how you can say that the answer to 1 is 1/3? If the first >>>>one is a boy, the other child has 50% chance of being a boy and 50% of being a >>>>girl, so that should be 1/2, instead! >>>> >>>> >>>>Serge Desmarais >>>> >>> >>>The reasoning for 1/3 must go something like this: There are four >>>possibilities for two children which we might specify as BB, BG, GB, >>>and GG, each of which is equally probable. Now, when we are told >>>that one is a boy, we must have one of BB, BG, GB (again each of >>>which has the same probability)--hence the 1/3 for BB. >>> >>>Another way of looking at it is to think about the set of all sibling >>>pairs in the world. Aproximately 1/4 will be BB, 1/2 BG or GB, and >>>1/4 GG. If we toss the GG's out of the set, then the BB's will be >>>1/3 of the remaining pairs. >>> >>>-Dan. >> >> Isn't it a little twisted? ONE of them is a boy, so BG or GB is the same in >>reality. Because the ONE that is a boy for sure is B, so the other is either B >>or G. Since there ar only 2 possible letters here and one is B, the question >>should be formulated as what are the chances for the other letter (kid) to also >>be B. Since no placement of the first mentionned B was specified, I would say >>that BG or GB is the same? >> >> >>Serge Desmarais >> > >It's definitely twisted. (I argued once with a friend for 15 minutes or so >about this--while driving a car, so I was somewhat distracted. He gradually >convinced me that it *might* be 1/3 and not 1/2--but I still had my doubts.) > >Let's change the meaning of the symbols so that BG means either BG or GB. >Now, in the collection of all sibling pairs approximately 1/4 will be >BB, 1/2 BG, and 1/4 GG. So we might have as representative sample of 8 >such pairs (BB BB BG BG BG BG GG GG)--which happens to obey just those >fractions. Now, if we consider only those in this sample which have a B >in them we have (BB BB BG BG BG BG), which as you can see has exactly >1/3 BB. > >Now, if we say the older of the two (assuming one of them is always older >than the other) is the B as in question (2, we need to go back to the old >notation so we can represent birth order: let the first letter in each pair >be for the younger and the second for the older. Then we would have >aproximately 1/4 each of BB, BG, GB, and GG. So our representative sample >could be (BB BB BG BG GB GB GG GG). Now, If we restrict this sample >to contain only those sibling pairs with an older boy we would have >(BB BB GB GB) which gives us 1/2 for BB. > >I guess what it boils down to is that probabilities have to do with a >lack of knowledge. A change in that lack may result in a change in the >probabilities. Question 2) implies an increase in our knowledge about >the situation (over the first question) and so the probablility goes >from 1/3 to 1/2. > >-Dan. So, since we know one is a boy (B), in 1/3 of the cases the second kid will be a boy, in 1/3 of the cases it will be a girl (G) and in the last third of cases, it will be ??? :) Serge Desmarais
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