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A letter & chan a andom from the alph
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Answer:
The first part is right, but the second part is wrong (although not an absolutely terrible estimate.)
Basically, when you do the trial n times, the value you computed is the expected number of occurrences of HAMLET.
This is a case where using the negative probability is better. The probability that you do not get HAMLET from one monkey is:
1−20!×2126!
So the probability that you don't get HAMLET from n monkeys is:
(1−20!×2126!)n
So the probability that you got at least one HAMLET from n monkeys is:
1−(1−20!×2126!)n
Solve for that ≥0.90.
I get n≥18175684.7….
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