Answer:
To solve this problem, we can use a Punnett square to determine the possible genotypes of the offspring.
First, let's assign the following letters to represent the alleles for fire-breathing and winged traits:
- F: allele for fire-breathing
- f: allele for not breathing fire
- W: allele for wings
- w: allele for no wings
The heterozygous fire-breathing dragon can be represented as Ff and the heterozygous winged dragon as Ww.
The Punnett square for this cross would look like:
```
| F f
---|-----
Ww | FW Ff
wW | fW ff
```
From this Punnett square, we can see that there are four possible genotypes for the offspring: FW, Ff, fW, and ff.
Out of these four possible genotypes, only one genotype (ff) would result in offspring that do not have wings and cannot breathe fire.
Therefore, the answer is: 1 out of 4 offspring will not have wings and cannot breathe fire.