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: $$H_0:\theta=.27.$$ 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 $$P(X \ge 33|H_0)=4.68*10^{-11}$$ 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 of 44 words to be unique was not observed by chance if the null hypothesis was true. 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.