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Home » General Discussions » Probability Problem

Probability Problem



Total possible scenarios: 7.
Scenarios of which both children are boys: 3.

Chance for two boys (in a world where children are only born on fridays and saturdays and given the information that one was a boy born on friday): 3/7

If you made a list like this for all 7 days of the week, you'd get 13/27. It's almost 50%, but not exactly.
  • Chiyuri wrote on 2011-09-08 03:51
    It's a Friday of unknown Day.

    Is it 8 April 2011? (Which is a Friday)

    or maybe it is 18 october 2003? (which is a Friday)

    maybe it's the legendary 29 Febuary 2008 (Which is a friday)


    Since the indication of which friday it is isn't writen, you can take every friday in existance as a possibility.
  • Kueh wrote on 2011-09-08 04:02
    Quote from Chiyuri;581657:
    It's a Friday of unknown Day.

    Is it 8 April 2011? (Which is a Friday)

    or maybe it is 18 october 2003? (which is a Friday)

    maybe it's the legendary 29 Febuary 2008 (Which is a friday)


    Since the indication of which friday it is isn't writen, you can take every friday in existance as a possibility.


    No, because the implication by not writing the date is simply that we are limiting the scope of the question to days of the week.

    You certainly could do the probability for every day of the year, and then multiple years, and then all the fridays that have ever passed. But that's not the question.
  • Sumpfkraut wrote on 2011-09-14 07:18
    They did not ask about the order of appearance, therefore it doesn't matter for this question, therefore there are only two options, ergo 50% chance.

    If you want to know the exact number of possible variations then that is a different problem which was not asked about, the formulation of the question very clearly indicates an I/O-problem. Tell your teacher to be more precise with his language the next time.


    And yes I do understand that there are two different "one boy"-variations and only one "two boys"-variation, which for all practical purposes would make it a 33% chance. I guess I'm a ***** for semantics or whatever.
  • Cucurbita wrote on 2011-09-14 07:28
    Quote from Sumpfkraut;586709:
    If you're really supposed to see a third option in a I/O-problem (either "one boy" or "two boys", the order of appearance doesn't strictly matter for the question) then all I can say is this is moronic and not even worth the label ivory tower maths. Having children isn't bloody quantum mechanics.

    Otherwise, your teacher gave you a really stupid example.

    They did not ask about the order of appearance, therefore it doesn't matter for this question, therefore there are only two options, ergo 50% chance.


    I was blown away by the lack of intelligence here.

    There never WAS consideration for order of appearance. The possibility is either A or B, so they can be exchanged in any way. But because they can be exchanged, their possibility remains.

    Girl Girl (impossible because one has to be a boy)
    Boy Girl
    Girl Boy
    Boy Boy (order does not matter)

    Therefore, there are 3 results, and only 1 of them fit the requirement.

    This is no different from the argument people are making for the monty hall problem. The real issue with the reason why people don't understand this question is because they can't properly define the term "probability" and can't comprehend what it means.

    IF, the question actually told you which one of the two born was male, then yes, the probability would be 50%. Because it rules out the possibility of one other option. For example, the question states "first born is male".

    Girl Girl (impossible)
    Girl Boy (impossible)
    Boy Girl (possible)
    Boy Boy (possible)

    Now its 50%.
  • Sumpfkraut wrote on 2011-09-14 07:37
    Erm no, it asks about "either one or two", not about "how many cases of one as opposed to two". I have edited my post since, I guess it was kind of weird before.

    It was presented as an I/O-problem, I approached it as such. I hope you can follow my weird train of thought with my revised post.

    I do realise it was kind of stupid though...
    Actually it was very much so. Oh well.

    It's all language games, isn't it~ :fail:
  • Cucurbita wrote on 2011-09-14 08:17
    Quote from Sumpfkraut;586721:
    Erm no, it asks about "either one or two", not about "how many cases of one as opposed to two". I have edited my post since, I guess it was kind of weird before.

    It was presented as an I/O-problem, I approached it as such.


    Still not understanding the meaning of probability.

    "That woman has two children, and at least one of them is a boy. What is the probability that she has two sons?"

    Order is unspecified. This is actually the easy part. Though it would fool the average person, anyone who has taken statistics should be able to tell you that the probability is not 50%, but rather 33.3%

    The real interesting point in this thread is the second question. It could probably fool even college stat students if they're not approaching the question carefully enough, though in the end I still have to say if they answer 33.3% for this one I think they deserve to fail the class on the spot. I myself almost jumped to that conclusion but then ended up thinking about it real hard and realized it was a trick question.

    arklian explained it very nicely here. If you don't understand it, just make a big spreadsheet on excel or something and see for yourself.

    For the record though, I've never taken a stats course. I did study it a whole bunch at one point, borrowing my sister's AP stats text. I do get to take college stats next semester, but I pretty much have most of it in memory.
  • Sumpfkraut wrote on 2011-09-14 15:24
    Quote from Cucurbita;586759:
    Still not understanding the meaning of probability.

    If you had actually read the post you quoted after my editing of it which I did mention, you would understand that I do understand.

    I was just caught up in a trick of language there. :fail:
  • whocares8128 wrote on 2011-09-15 04:00
    Quote from Joker;581574:
    Well?


    Assuming the host always opens a door with a goat before then always offering the chance to switch, yes, switching increases the chance of getting a car from 1/3 to 2/3.
  • Cucurbita wrote on 2011-09-15 05:26
    Quote from whocares8128;587439:
    Assuming the host always opens a door with a goat before then always offering the chance to switch, yes, switching increases the chance of getting a car from 1/3 to 2/3.


    Question I asked in the thread this thread is based off of is more or less the same question but with a different example.

    That was one wild ride we went on. People were ready to fight to the death to argue that the result is 50% whether or not you switch.

    I suppose its a good way to separate those who have the ability to think on a higher level and those who don't.