A riddle my brother gave me today

by bohm 101 Replies latest jw friends

• 

  bohm

  Argh, i hate hate hate google.

  The solution is quite simple. My brother solved it by a counting argument, but i think the most obvious thing is to use bayes theorem which is what i did. here goes:

  SOLUTION:

  The right answer is 13/27. If we neglect the information about tuesday, the answer is 1/3 - the combinations are BG, GB, BB, and GG, GG is obvisouly out of the question since he has at least one boy, which leave the 3 other combinations. Only one of those has two boyes, hence 1/3.

  BUT if we get the information about the day of birth that is wrong. Why?

  Imagine the man had said: I have two children, one is the kid who run around just on top of that hill, what is the probability the other is a boy to?

  Obviously the answer is 1/2 here, since the chance both kids is the kid on top of the hill is zero. So intuitively, the answer is between 1/2 and 1/3.

  However, the exact result is very easy to calculate. What we want to compute is this:

  P(2 boys | one is a boy, born on tuesday)

  By bayes theorem

  P(2 boys | one is a boy, born on tuesday) = P( one is a boy, born on tuesday | 2 boys) p(2 boys) / P( one is a boy, born on tuesday)

  Its now easy to compute:

  P( one is a boy, born on tuesday | 2 boys) = P( one is born on tuesday) = 1-P( none is born on tuesday ) = 1-(1-1/7)^2

  P( one is a boy, born on tuesday ) = 1 - (1-1/14)^2

  p(2 boys) = 1/4

  Which give the right result.

  So here is the roundup. Albert wins the price for a correct answer. ML wins the prize for best numerical estimate, and snowbird win the prize for closest to the actual argument by giving 1/3. Duncan and StAnn wins the price of best googling skills.

  John Doe and The Silence wins the "shouldnt have talked so much about my math major prize" - JD, where did you go? Am i still wrong?

  and i allmost won a beer...
• 

  bohm

  just wanted to bump this up for the night audience, in case anyone want to pass it along.
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  John Doe

  Ok, I'm back. Worked overtime last night and didn't get home until 3 am.

  First of all, I want to acknowledge that I was incorrect. I made a simple assumption that was not supported by the puzzle; namely, that the first child was the boy. The information I gave regarding coin toss statistics is correct, but I did not apply it correctly to this problem. When you automatically assume which child is a boy, it eliminates potential outcomes, as has been pointed out.

  "

  A probability is nothing more than the ratio of an occurence to non occurence. This is determined solely by the enumeration of possible outcomes. A particular occurance in a specific chance has no bearing on the probability of the next occurance. Therefore, the statement that the more boys you have the higher the chance the next one will be a boy is patently and conclusively false."

  Now lets review my actual statement:

  Why? Your actual statement was not under consideration. I was solely speaking about changeling's statement and your saying that her statement was only incorrect under some conditions. Hence "the statement." Or, are you saying I misread changeling?

  Side note for changeling: You are right, ff one assume a given couple generate boys with a probability a, the more boys they have (compared to girls) the higher our estimate of a will be, and we will estimate the probability their next children is a boy to be higher. a does not increase exponentially, though.

  In the problem, we neglect this effect and assume a=1/2 for both births. Ie. i ask the problem under the most simple assumptions.

  So its pretty damn clear i never wrote the probability the next will be a boy will be higher, i wrote our belief the next will be a boy will increase. That you begin your post by writing that: "You stated the assumption was that the probability of having a boy is 1/2. " is a red herring, since i clearly indicated that i was NOT discussing the riddle with my post by my last statement which i have underlined.

  "Belief" has nothing to do with the problem as worded--it is strictly one of statistics. Probability is probability.
• 

  streets76

  I was born in the backseat of a greyhound bus.
• 

  bohm

  John Doe:

  Well...

  Changelings statement is wrong when you read it litterally for a lot of reasons. I believe this is because Changeling is not used to expressing herself in mathematical terms, and use her intuitive interpretation of the words "probability", "chance", etc. I choose not to jump up like a smug smartass geek and cry: "Your wrong!!!" because i see no point in that. I understood changelings remark to mean what i wrote here:

  You are right, ff one assume a given couple generate boys with a probability a, the more boys they have (compared to girls) the higher our estimate of a will be, and we will estimate the probability their next children is a boy to be higher. a does not increase exponentially, though.

  Notice my statement is different from Changeling, but i think changeling is trying to say what i wrote: If a women give birth to 6 children, all of which are boys, we would say the chances that the next is a boy is more than 1/2. Read it carefully. i dont say the probability she has a boy change, i say our belief she has a boy DO. So let me be abselutely clear (but uncivil to changeling): I defend the statements i have formulated, not changelings, because they are obviously wrong since she lived a life instead of taking math courses. If you see any problems i will be happy to discuss them.

  And by the way - since it seem you are our with the fine comb, you wrote to me: "Belief" has nothing to do with the problem as worded--it is strictly one of statistics. Probability is probability.

  Probability is probability, but its also what you defined it to be earlier:

  A probability is nothing more than the ratio of an occurence to non occurence. This is determined solely by the enumeration of possible outcomes.

  a couple of things here. First off, when talking about the probability the next child will be a boy, what are the occurances and non-occurances exactly you use to calculate that ratio?. Secondly, it would seem we have at most one occurance, namely one future birth.

  At any rate this seem to come down to belief a given event will occur, which is then again based on our subjective knowledge.

  i will be happy to hear you elaborate on this without copy-pasting :-).
• 

  StAnn

  EXCUSE ME, Bohm, I didn't google the answer. I spent 30 minutes working the stupid thing out on paper.

  I'm offended.

  I was the first one to come up with the right answer and you just disregarded me. Consider yourself SPANKED.

  StAnn
• 

  bohm

  StAnn, Im very very sorry! I nominate you as the winner, and i count myself honered to be spanked by the hand who worked out the solution!

  are you by any chance NOT a math major?
• 

  besty

  great thread bohm - I love these kinds of puzzles - reminds me of the Monty Hall Problem made famous in the movie 21.
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  StAnn

  Bohm, not only am I NOT a math major: I'm an ART major.

  StAnn
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  John Doe

  a couple of things here. First off, when talking about the probability the next child will be a boy, what are the occurances and non-occurances exactly you use to calculate that ratio?. Secondly, it would seem we have at most one occurance, namely one future birth.

  At any rate this seem to come down to belief a given event will occur, which is then again based on our subjective knowledge.

  i will be happy to hear you elaborate on this without copy-pasting :-).

  If I copy paste, I divulge the fact when doing so. You can be certain I did not use google in my posts--had I done so, I would not have been mistaken.

  I should have been more clear. Pay attention to the last sentence you quoted:

  This is determined solely by the enumeration of possible outcomes.

  "Possible" outcomes are not "actual" outcomes. Do I need to elaborate further?