I think that the term 'by chance' is not clearly defined as long as you do not have a specific hypothesis you want to test. 

You could regard the full text as your population. The complete 'census' of all words resulted in the 'true' parameter $\theta=.27$, say. 

Now you describe that you took a 'sample' of words, whose characteristic is page position (first word on each page) and you want to test the hypothesis, whether page position affects the propbability of a word being unique. 

Hence you want to test: $$H_0:\theta=.27$$ which is equivalent to asking whether the sample of words comes from the population of all words (your full text) or forms an own (sub-) population. 

If we regard the 44 pages (words) as independent draws from a Bernoulli distribution, the number of positive outcomes $X$ is Binmoial. Now we need 

$$P(X \ge 33|H_0) \approx 4.68*10^{-11}$$ 

As you can verify using R `pbinom(32,44,.27,lower.tail=FALSE)`. This probability is very small, so you can say with very low probability of error that observing 33 unique of 44 words was not caused by chance alome, *if the null hypothesis was true*. Hence, $\theta$ of the sub-population of words at the top of all pages seems to be different from your population $\theta$ of .27. 

Put differently, position seems to have an impact on the probablity of uniqueness. Only in a very small proportion of cases you would make an error when claiming this.