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
    that
    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
    #1
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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
    #2
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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
    #3
  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
    #4
  5. Im not sure if this is right, but i remember problem like this...here
    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
    down:

    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

    BL/BL
    BL/br
    BL/BL
    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

    br/BL
    br/br
    br/BL
    br/br

    Youd have a 50/50 chance of getting a brown rat...
     
    [email protected], Sep 22, 2004
    #5
  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

    --
    Bob O'Hara

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

    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: http://www.jnr-eeb.org
     
    Anon., Sep 22, 2004
    #6
  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
    #7
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