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Genotypes of original parents: XmXm (female) Xm+ (male)
F1 Results:
Females: XmXm+ (long wings) (0 miniature : 1 long)
Males: Xm (miniature wings) (1 miniature : 0 long)
F2 results:
Females: 50% XmXm (miniature wings), 50% XmXm+ (long wings) (1 miniature : 1 long)
Males: 50% Xm (miniature wings), 50% Xm+ (long wings) (1 miniature : 1 long)
How to figure this out:
Females have 2 X chromosomes, and males have 1. This means that the male fly (normal wings, same thing as long wings here) must have one gene that matches his phenotype, so he's Xm+. The female has miniature wings, and you know that that is recessive, so she must have two identical copies of the recessive gene, so she is XmXm.
The male offspring of any cross will get one of the female's X's. It's random as to which he'll get. In the first cross, the female only has one possible X, so all of the male offspring get that. In the second cross, the female has two different X chromosomes, so it's 50/50 as to which each son ends up with. This means that 50% will have one, and 50% will have the other.
The female offspring of any cross always get the male's X, and one of the female's X's (again, it is completely random as to which of the female's X's the daughters receive). With the first cross, the female only has one kind of X, so the daughters all receive that X and the male's X. In the second cross, the female has two kinds of X, so the daughters have a 50/50 chance of getting either of those X's, and then also receive the male's X.
Figuring out the phenotypes is simple. For males, their phenotype matches the genotype of the one X that they have. For females, if Xm+ is present at all, they will have long wings. If both X's are XmXm, then they will have miniature wings.
Note: It can sometimes help to "track" the Y chromosome along with the X chromosomes when dealing with sex-linked genes. It depends on your teacher's preference; if you feel your teacher wants you to keep track of it as well, add in a "Y" to every male genotype.
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