Tongue rolling is due to a dominant allele. Of two sisters in a family, one is a

First, let's define our alleles:

D = can roll tongue (dominant)
d = cannot roll tongue (recessive)

Possible genotypes:

DD (can roll tongue)

Dd (can roll tongue)

dd (cannot roll tongue)

It is mentioned that the mother cannot roll her tongue, therefore she must have the genotype dd.  The father's genotype must be Dd, which would result in one of his daughters that can roll her tongue and the other which cannot. 

P1 Cross: Dd (father) x dd (mother) 1/2 Dd (daughter 1) & 1/2 dd (daughter 2)

Hope this helps! 

The mother is homogeneous because she can't roll her tongue and in order for her to do so she must have two recessive alleles for this trait. The father is heterogeneous because he can roll his tongue, therefore he must carry the dominant allele to enable him to do so. However we know that he also carries the recessive allele because one of his daughters can't roll her tongue, meaning that she recieved a recessive allele from each parent. This daughter who can't roll her tongue is clearly homogeneous recessive just like her mother because she must have the two recessive alleles to have this trait. The other daughter is heterogeneous just like the father because she must have the dominant allele in order to be able to roll her tongue but she also had to have recieved a recessive allele from her mother because that is the only type of allele her mother carried.

Tongue rolling is due to a dominant allele. Of two sisters in a family, one is a tongue roller and the other is not. Their mother cannot roll her tongue. What is the genotype of each of the sisters and the father?

One of the sisters cannot roll her tongue, which means she is "dd". The mother cannot role her tongue either, so she is also "dd". This means that the other sister must be Dd, because one allele must be dominant while the other is recessive (because that is all that the mother can give). The father, therefore, must be Dd. He cannot be DD because then both daughters would be tongue rollers.

The mother is dd. Sister 1 is dd. The father must be Dd and not DD because if he were DD, his daughters would be tongue rollers, and would be Dd.