Help with simple probability question!! Excellent question.

Discussion in 'Scientific Statistics Math' started by Duke Morrison, Sep 20, 2004.

  1. Q: In a certain species of rats, black dominates over brown. Suppose
    a black rat with two black parents has a brown sibling.
    (a) What is the probability that this rat is a pure black rat
    (as opposed to being a hybrid with one black and one
    brown gene)?
    (b) Suppose that when the black rat is mated with a brown
    rat, all five of their offspring are black. Now, what is the
    probability that the rat is a pure black rat?

    An answer to this question would be greatly appreciated... I have a
    hunch that the answers are 1/3 and .94 but cannot fully confirm
    this... they could be wrong. If anyone has a descriptive solution to
    this question I'll forever be in your debt. Thank you!
    Duke Morrison, Sep 20, 2004
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  2. Please do not bother with answering this question as I have now
    confirmed my answer properly. But thanks to all those who took the
    time to read it anyways. =]
    The answer is indeed 1/3 and .94 for all those interested.
    Duke Morrison, Sep 21, 2004
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  3. No answer can be derived unless we know the prior probabilities
    of black, brown, and hybrid rats. (Rats!) ~ George Kahrimanis
    George Kahrimanis, Sep 21, 2004
  4. Duke Morrison

    Henry Guest

    Not in this case. We are suppose to conclude that the parents were
    both hybrids and proceed from there.
    Henry, Sep 21, 2004
  5. Im not sure if this is right, but i remember problem like
    my guess

    here are the possible break-downs of one rat with vaiables for x and y
    chromosomes(BL = domanant Black, br
    = ressive brown):

    BL/BL = pure bred black rat
    BL/br = hybrid black rat
    br/BL = hybrid black rat
    br/br = pure bred brown rat

    Considering that both parents are hybrids, this would be the new break

    BL/br x BL/br (order doesnt matter really)

    This now gives us these possibilities (by FOIL method):

    BL/BL = pure bred black rat
    BL/br = hybrid black rat
    br/BL = hybrid black rat
    br/br = pure bred brown rat

    So the answer is that the probability of getting a brown rat from two
    hybrid black parents is 1 out of 4.

    If, just as a side note, if the parents were a pure bred black rat
    (BL/BL) and a hybrid black rat (BL/br or br/BL), the possibilities
    would look like this:

    BL/BL x BL/br


    so it be impossible for a brown rat to be born with those parents
    because BL is domanant. However if the parents were a Pure bred Brown
    rat (br/br)and an hybrid
    rat (BL/br)

    br/br x BL/br


    Youd have a 50/50 chance of getting a brown rat...
    [email protected], Sep 22, 2004
  6. Duke Morrison

    Anon. Guest

    Which is true, but you still need to know the genetics of the system.
    If two genes are involved (and a rat has to be homozygous recessive at
    both loci to be brown), then you get a very different result.

    As we don't know the genetics, we have to integrate over the
    probabilities of different systems, so George is right in that sense too!

    The take-home message: anyone writing a homework question should make
    sure they give all of the information needed to answer the question.


    Bob O'Hara

    Dept. of Mathematics and Statistics
    P.O. Box 68 (Gustaf Hällströmin katu 2b)
    FIN-00014 University of Helsinki

    Telephone: +358-9-191 51479
    Mobile: +358 50 599 0540
    Fax: +358-9-191 51400
    WWW: http://www.RNI.Helsinki.FI/~boh/
    Journal of Negative Results - EEB:
    Anon., Sep 22, 2004
  7. I am sorry. I need to install a time-delay to my postings, with an
    "Are you sure?" window. Thanks for the correction, Henry.
    George Kahrimanis, Sep 22, 2004
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