Monkeys to write shakespear.

I was curious about the actual amount of monkeys needed to produce something like hamlet, so I went and figured out how many letters there were: 194270

There are 26 letters in the alphabet so every possible combination of letter we can have in hamlet:

$\displaystyle 26(194270)=5051020$

This problem produces a binomial distribution, so the mean of the normal curve would

be 1 because:

$\displaystyle \mu=np=(5051020)(5051020)^{-1}$

$\displaystyle \sigma = \sqrt{npq}=\sqrt{1(0.999999802020186)}$

$\displaystyle P(X\geqslant 1)=1-P(X\leqslant 1})$

$\displaystyle 1-P(Z\leqslant \frac{1-1}{\sigma })$

$\displaystyle 1-P(Z\leqslant 0})=1-.5=.5$

Therefore, if we have 5051020 monkeys, the probability of one of them producing hamlet (asssuming each only gets one try, the typing of one monkey does not effect the typing of another, and the probability of each monkey geting hamlet is the same) is on average 50%.

Is this correct?