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  • The boy-girl puzzle
  • Smee
    Free Member

    Go and get two coins.

    What are the chances of the first one being a head? 50:50
    What are the chances of the second one being a head? 50:50

    If you dont know any of the results then all 4 permutations have a 25% chance of happening.

    After the first result is known they have a 50% chance.

    funkynick
    Full Member

    Look Smee, you have a friend… 😀

    By the way, you never did answer me about whether an older girl/younger boy is really the same as an older boy/younger girl…

    GrahamS
    Full Member

    Yes yes Smee those are independent events. Everyone agrees that, as explained 16 times already.

    the first result doesn’t influence the second. No one disputes that either.

    But you don’t know the “first result”, you know one of the results.
    That is very different.

    Try my 100 coin toss. Explain the results on my spreadsheet.
    Or come up with an experiment that matches the question.

    GrahamS
    Full Member

    How about this then: you agreed above that before you know any results then all four coin combinations have a 25% chance.

    So how about I throw the coins and I then tell you “I didn’t throw two tails”
    What are the odds on the other combinations now?

    Drac
    Full Member

    What are the chances of the first one being a head? 50:50
    What are the chances of the second one being a head? 50:50

    If you dont know any of the results then all 4 permutations have a 25% chance of happening.

    After the first result is known they have a 50% chance.

    I can’t believe you don’t grasp the coin one.

    Wiredchops
    Free Member

    Come on lads, this isn’t over, we can stretch it for another day!

    miketually
    Free Member

    Smee, at some point we need to meet up and do this with coins. I’ll bring 50 £1 coins and you bring 50 £1 coins.

    If there’s two tails, you get to keep the coins. If there’s one of each, I get to keep them. If you’re right, we’ll both come out even.

    If you’re right, we’ll both leave with ~£50. If the rest of the planet is right, I’ll leave with ~£67 and you’ll leave with ~£33.

    WackoAK
    Free Member
    Wiredchops
    Free Member

    Surely smee would not dare doubt the wisdom of Dr Math!?

    GrahamS
    Full Member

    Come on lads, this isn’t over, we can stretch it for another day!

    250 replies is respectable, but I’m still hoping for my first Triple Century posting. 😀

    WorldClassAccident
    Free Member

    What happens if we use 20p peices instead of £1 coins?

    Would this reduce the odds to 20% or 66%?

    miketually
    Free Member

    From the Dr Math site: “We can also visualize this problem using a probability tree”

    Gosh, they look familiar. Mine were prettier though.

    Drac
    Full Member

    right, final answer here
    http://mathforum.org/dr.math/faq/faq.boy.girl.html

    But it’s wrong the maths wrong, Smee said so.

    I know why he’s confused I was at first but I never claimed to be right just couldn’t see why it wasn’t 50/50 1:1 50%. Then it suddenly sunk in that’s it’s the lack of specify which child that increases the odds, the same way the order the lottery numbers comes out doesn’t matter therefore increasing the odds.

    Steelfreak
    Free Member

    Hummm…

    I think I’m beginning to understand how the global economy became f*****.

    Wiredchops
    Free Member

    Population too high? Not enough parents with two girls? I think I’m with you here.

    GrahamS
    Full Member

    I think I’m beginning to understand how the global economy became f*****.

    I don’t think you can blame Smee for that one.

    matthewjb
    Free Member

    I think I’m beginning to understand how the global economy became f*****.

    I don’t think you can blame Smee for that one.

    I think you can if he’s been teaching the banks how to do sums.

    theflatboy
    Free Member

    when you know that one is a h you have:
    one of ht or th – not both.

    if you have 1 x 10p and 1 x 2p, then quite clearly 10p heads, 2p tails is not the same as 10p tails, 2p heads. hence two different ways of getting one heads and one tails. therefore twice as likely as getting 10p heads and 2p heads. is this getting through to you?

    Rona
    Full Member

    Lets get it over 300.

    It can be 50%, here’s how.

    What you want to know is whether “she has a girl and a boy?”. You can find this out by finding out the gender of both children. As you already know the gender of 1 child you only need to know the gender of the other child. As the only unknown is the gender of 1 child where the two possible outcomes each have a probability of 50% you can determine whether “she has a girl and a boy?” with a probability of 50%.

    Andy.

    GrahamS
    Full Member

    What you want to know is whether “she has a girl and a boy?”.

    Nope – that’s not what the question asked.

    The question is about whether her responding that she has at least one girl changes the probability that she is in the group that have one child of each sex. And it does.

    If the question said “Here is a woman with a daughter, what is the gender of her other child?” then it would have been a straight 50:50 – but that is a very different question.

    GrahamS
    Full Member

    Also.. Rona is a girl’s name. 😛

    taka
    Free Member

    hi just for the next post

    spoon
    Free Member

    GrahamS is quite correct.

    The way the question is asked/worded provides 2 very different answers.

    spoon
    Free Member

    Oooh reading back a few pages, quite a few people are correct apologies.

    GrahamS
    Full Member

    Yeah, it’s pretty much just been Smee that hasn’t seen the light so far.
    Everyone else has got there – as I’m sure Rona will 🙂

    Drac
    Full Member

    Funny how this is Rona’s first ever post.

    Rona
    Full Member

    Drac, been here a very long time.

    Graham,

    “What you want to know is whether “she has a girl and a boy?”.

    Nope – that’s not what the question asked.”

    No, indeed but that’s why probability is only probability, if you ask a different but relevant question to get the information you need you may get a different probability, i.e. as pointed out before the odds that the remaining child is a boy are 50:50 by simply asking that question the probability of her having a girl and a boy are 50:50.

    Andy.

    Rona
    Full Member

    not too many to go now. . .

    Drac
    Full Member

    Drac, been here a very long time.

    Took you a month to post though.

    Rona
    Full Member

    It’s been pretty dull.

    Drac
    Full Member

    Sorry I’m being sceptical spent too long on many forums and always cautious when a dormant member suddenly starts posting on dying threads.

    GrahamS
    Full Member

    Well yes, probabilities are based on the information you have. if you ask different questions then you gain different information and you get different probabilities.

    You could have simply asked her “Do you have a son and a daughter?” and, assuming that she is telling the truth then the probability is 100% that she does. That doesn’t mean that if you’d asked her the original question instead that the probability would be anything other than 66%.

    Stu
    Full Member

    Rona
    Full Member

    Yes, but why would you ask her the original question? If you were speaking to her you’d ask a much more sensible question which would confirm the probability is 50% :-).

    Andy.

    schroedingers-cat
    Free Member

    I’ve got three kids and they are all boys, does that help at all?

    Drac
    Full Member

    Yes, but why would you ask her the original question?

    For the interests of science.

    miketually
    Free Member

    Yes, but why would you ask her the original question?

    So you can find out who the less intelligent people are.

    Smee
    Free Member

    42.

    GrahamS
    Full Member

    Smee! You’re back. There is hope for this thread yet.

    Go on, give me an answer to some of the questions put to you.
    I’m particularly interested to see how you answer the “I didn’t throw two tails” scenario or flatboys 2p and 10p.

    Smee
    Free Member

    Ever heard the saying “holding the cat’s arse to the sun?”

Viewing 40 posts - 241 through 280 (of 463 total)

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