Riddle -- Probability of Expectation

I was given a sheet of riddles for extra credit in my statistics class and got all but one of them right.

Here's the one that totally stumped me and pissed me off.

In The Art of Shakespeare's Sonnets (Harvard Univ. Press, 1997), author Helen Vendler noted that each of the 14 lines of Sonnet 20 (one of 154 sonnets written by Shakespeare) includes the letters of the word "hues" and or the letters of the word "hews."

Suppose that 154 monkeys sitting at 154 keyboards pounded out one sonnet apiece, each consisting of 14 lines and 36 alphabet letters each, with each letter equally likely. What is the probability that in at least one of the sonnets, every line includes the letters of the word "hues" and/or the letters of the word "hews?"

What say youse?

Prof. will not be giving the answer until the end of the semester.