Fraternal Twins

Discussion in 'Games Forum' started by rstrats, Apr 5, 2014.

  1. rstrats

    rstrats
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    A woman is about to give birth to fraternal twins. What is the chance that one of the twins will be a girl?​
     
  2. Don

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    About 2/3?
     
  3. TCassidy

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    About 50-50.
     
  4. Deacon

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    Chances

    Girl - Girl
    Girl - Boy
    Boy - Girl
    Boy - Boy


    Odds are 75% at least one will be a girl.

    Rob
     
  5. Don

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    I'd argue that your options 2 and 3 are the same; thus, 2 out of 3....
     
  6. Don

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    Although, I do accept that it also depends on which came out first, so I understand 75%....
     
  7. Deacon

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    Now I know Dr. Cassidy as a very precise person on the BB - he reads things exactly as they are written.

    The question as raised in the OP was, "What is the chance that one of the twins will be a girl?"

    As he noted, there is a 50% chance that only one will be a girl.

    Rob
     
  8. rstrats

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    Deacon,

    re: "Odds are 75% at least one will be a girl."


    And the interesting thing is that there is also a 75% chance that one of the twins will be a boy.
     
  9. Don

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    With al due respect to Dr. Cassidy and you -- incorrect. First, the opening post did not specify "only" one. Second, in accordance with the wording of the opening post, girl/girl is a valid option, raising the odds to 66% instead of 50%. If the opening post had specified "only" one is a girl, then the options would be limited to boy/boy and boy/girl, resulting in 50%. If the opening post had specified the birth order, then Deacon's 75% would be valid. But a strict reading of the opening post leaves only the 2 out of 3 option.
     
  10. Don

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    Well...my apologies. The question is more complex than I originally thought.

    On the one hand, with twin comparisons, the answer is 66%. However, if one starts using truth tables, you get:
    B G
    B F T
    G T T
    (B-boy, G-girl, T-true, F-false)
    And thus, 75%.

    Alternatively, upon birth of the first child, if it's a boy, there's a 50% chance the next child will be a girl. If the first child is a girl, then we've reached 100% probability. The average of these two alternatives is also 75%.

    You could make it even more difficult, and throw in the probability that 40% of twins are boy/girl, leaving 30% equally for boy/boy and girl/girl (except that statistically, boy/boy twins miscarry more than girl/girl, so that actually increases the odds of a girl child....)

    In the end analysis, I should probably apologize to Deacon and go with the 75%....
     
  11. rstrats

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    Don,

    re: "In the end analysis, I should ...go with the 75%...."


    That is correct. As you noted, there are 4 possible combinations and a girl shows up in 3 of them.
     
  12. rstrats

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    And the more interesting thing is that a boy also shows up in 3 of the combinations.
     

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