This is a question about the availability of genetic tests that distinguish full siblings (such as sisters with the same mother and father) from half siblings (such as sisters with the same mother but different fathers). Although full siblings, like parent-child pairs, share half of their alleles, the analysis is a bit trickier. Consider these examples:
The numbers here represents the allelic state of one marker. Each child inherits one allele (one version of the marker) from each parent. In this example, Amy has inherited allele 1 from her father and allele 3 from her mother. Because children must share one allele with each of their parents it is relatively easy to rule out paternity. For example, P2 cannot be Brooke's father because he has completely different alleles from her (1 and 5 vs. 2 and 3). Unlike parents and their children, full siblings can have completely different alleles (e.g. Amy and Casey). Since the question refers to three sisters, it would be possible to rule out all three having the same father (e.g. sisters with genotype 1/3 (Amy), 2/3 (Brooke) and 5/3 (Dawn) cannot all be full sisters because there are three different alleles in combination with the 3, and a single parent can only contribute two possible alleles). However, this is not always the case, and it is even possible for half-sisters to have the same genotype at any one marker (e.g. Amy and Erin) because any two possible fathers could share one or two alleles by chance.Thus, distinguishing full-siblings from half-siblings comes down to statistics, and "results" are reported as probabilities. Since that is the case, the more markers the better. Many of the genetic testing services probably aren't using enough markers (but they do provide guidance as to how (un)reliable their result is). On the other hand, a full genotyping service, like 23andme, which uses thousands of markers, would provide a reliable result. So, the bottom line is yes, you can determine, with confidence, whether three sisters have the same father by testing the sisters. However, you need to use a lot of markers to do it, and most genetics testing companies probably don't use enough. If you're going to have the testing done, ask the testing service how many markers they use.
