# Help with simple probability question!! Excellent question.

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

1. ### Duke MorrisonGuest

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

2. ### Duke MorrisonGuest

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

3. ### George KahrimanisGuest

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. ### HenryGuest

Not in this case. We are suppose to conclude that the parents were
both hybrids and proceed from there.

Henry, Sep 21, 2004
5. ### [email protected]Guest

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...

Sep 22, 2004
6. ### 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
7. ### George KahrimanisGuest

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