You might notice that, if you fix the number of successes and the number of trials, the pmfs are proportional. This ties into the so-called Likelihood Principle. Because of this relationship, if you accept the LP it essentially means that whether you observe a negative binomial process or a binomial process you should make the same inference about the success probability.

I'm not sure if this is what is being looked for by your instructor, but the LP is a very important concept (IMHO) and the relationship between the binomial and negative binomial is often how it is introduced.

See example 1 of this for a short discussion of this particular problem (negative binomial and binomial).