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Does muliplication Rule of probability apply on sexes?

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Does muliplication Rule of probability apply on sexes?

Postby potatoyuu » Sun Mar 20, 2011 10:58 am

I am reading two Biology text books and it seems to me like they conflict their veiws on some of the probability problems.

Campbell's Biology said
"To find the probability of two independent events happening, multiply the chance of one happening by the chance that the other will happen.
For example, the chance of a couple having two boys depends on two independent events.
The chance of the first child being a boy is 1/2; and the chance of the next child being a boy is 1/2.
The chance that the couple will have two boys is therefore 1/2 x 1/2 = 1/4.
The chance of having three boys is 1/2 x 1/2 x 1/2 = 1/8."

Here is a sample problem and solution form Baron's Biology.

"A couple has 6 children, all girls. If the mother gives birth to a seventh child, what is the probability that the sevent child will be a girl?"
a) 6/7
b) 1/128
c) 1/2
d) 1

Following the Multiply Rule; 2^7 = 1/128, therfore (B) would be the answer.

And here comes the problem; The Answer accordingto Baron is (C), becuase No matter how many children a couple has, the chance that the child will be aboy or a girl is always 1/2. Although it is true that whether the sperm carries an X or a Y sex chromosome dtermins the sex of the child, that is irrelevant to the question here.

Can you clear my thoughts on this, please?
Thank you.

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Postby Darby » Sun Mar 20, 2011 10:43 pm

I've run into this before - there is a statistics of conjoined events, which the "It's always one out of two" disagrees with. It may be a matter of perspective.

Hey, it's statistics, it seems like it should make sense, but it often doesn't. I just know that I learned the multiply rule in an actual statistics course...
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Postby canalon » Mon Mar 21, 2011 10:20 pm

This is because you are looking at 2 veryy different questions:
In Campbell's they calculate the probability that all kids are of the same sex, in Baron's they are looking at the probability for the 7th kid to be of a given sex.
The basic assumption behind each question is that each draw is an independant event whose probability is therefore constant no matter the number of draws (Baron) which allow the calculation of a given series of particular events as the product of the individual probabilities.

Darby I would have expected better from one of our older member with usually good and level headed abilities :p
I hate stats but they are not despicable tools of the devil made to annoy people. They are valuable tools with so many cutting edges that they must be handled very carefully, and then they can do magic. Actually it just in par with juggling with burning working chain saws blidfolded while staying afloat on an unstable raft on lake of gasoline. Basic science skillset ;)

Science has proof without any certainty. Creationists have certainty without
any proof. (Ashley Montague)
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Postby Darby » Tue Mar 22, 2011 1:56 am

I think of all of the tools in the toolbox of science, they are the ones that are most often misused or used irresponsibly. They are valuable, but easy to mistrust.
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Postby JackBean » Mon Mar 28, 2011 10:09 am

potatoyuu: how would you calculate the probability, that they will have 7 girls and 1 boy? As
So, here you see all your odds for particular cases (i.e. girl in the first case, girl in the second case ... and boy in the eigth case;)

Cis or trans? That's what matters.
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