how to use polynomial to model combinations

Question

Would you please show me how to solve this story problem.

 

Eye color is determined by genetic combination.  Let R represent the gene for brown eyes and l represent the gene for blue eyes.  Any gene combination including R results in brown eyes.  Consider the offspring of a parent with a homozygous brown-eyed RR, gene combination and a parent with a teterozygous brown-eyed, Rl, gene combination.

 

1.  How would I show that you can use a polynomial to model the possible genetic cominations of the offspring?

 

 

2.  How do I solve to find the percent of possible genetic cominations result in brown-eyed offspring?

 

3.  How do I find the percent of the possible genetic combinations are carriers for the blue-eyed gene?

 

 

Thanks!!!

Answer 1

1. (R + R)(R + I) = 2R(R+I) = 2R^2 + 2RI = RR + RR + RI + RI

 

2. "Any gene combination including R results in brown eyes."

Since 4 out of the 4 possible combinations have an R the probability is 100%.

 

3. Since 2 out of 4 possible combinations have an I the probability is 50%.

Answer 2

Hi L;

(parent)(parent)=total combinations

(R+R)(R+I)=total combinations

Let's FOIL...

FIRST...(R)(R)=R²

OUTER...(R)(I)=RI

INNER...(R)(R)=R²

LAST...(R)(I)=RI

R²+RI+R²+RI=total combinations

2R²+2RI=total combinations

R²+2RI=brown-eyed

II=0, not represented in equation.