You have one tree that produces big yellow apples and another tree that produces small red apples. when the two are crossed, you find that half the offspring trees produce big red apples and half produce big yellow apples. what are the genotypes of the parents?

This is the complete question.

Assume that there is a gene in apples that determines fruit color and a second gene that determines fruit size. Let A represent the dominant allele for big apples, and a represent the recessive allele for small apples. Similarly, let R represent the dominant allele for red apples, and r represent the recessive allele for yellow apples. You have one tree that produces big yellow apples and another tree that produces small red apples. When the two are crossed, you find that half of the new trees produce big red apples and half produce big yellow apples. What are the genotypes of the parents?  

AArr and aaRr

Explanation:

From the question, we are given that;

Let A represent the dominant allele for big apples; &

a represent the recessive allele for small apples.

Similarly, let R represent the dominant allele for red apples; &

r represent the recessive allele for yellow apples.  

After Crossing, half of the new trees produces Big red apples (i.e AaRr or AARR) & Half produce big yellow apples (i.e Aarr or AArr)

Now, lets assume that the genotypes of the parents are AArr and aaRr

If AArr self crossed; we have = ( Ar, Ar, Ar, Ar)

aaRr will be ( aR, ar, aR, ar)

Now, if these F1 offspring crossed, we have;

         Ar          Ar          Ar          Ar

aR     AaRr     AaRr      AaRr      AaRr

ar      Aarr     Aarr        Aarr       Aarr

aR     AaRr     AaRr      AaRr      AaRr

ar      Aarr       Aarr      Aarr        Aarr

From above, we can see that; we have the 8 offspring possessing AaRr genotypes and Aarr genotypes.

8 AaRr : 8 Aarr

AaRr implies big red apples as; A-a (heterozygous for  big apple allele mask the effect of the recessive small allele which makes it to be dominant  big apple).

Also R-r (heterozygous for red allele mask the effect of the recessive yellow allele which makes it to be dominant red color)

On the other hand, Aarr implies Big yellow apples as; A-a (heterozygous for  big apple allele mask the effect of the recessive small allele which makes it to be dominant  big apple).

Also rr  = (recessive yellow traits)

Therefore, from the foregoing we can conclude that the progenitor whose genotypes are AArr and aaRr   are the right match to produce  half of the  offspring trees with big red apples and half offspring trees with big yellow apples.