Question

Misprints are distributed randomly and uniformly in a book at a rate of 2 per 100 lines. What is the probability that a line is free of misprints?

Answer 1

I thought this was simply saying that 2 lines of 100 have errors
So, there are 100-2=98 lines out of 100 that are error free (on avg. )

So, Probability = 98/100 = 0.98

But, my book uses a Poisson distribution: Let X be the # of errors

\(\mu=\lambda t\) where \(\lambda\) = 0.02/line, \(t\) = 1 line, so \(\mu\)=0.02

\[P(X=0)=\frac{(0.02)^0e^{-0.02}}{0!}\]=0.9802 (which is still close to 0.98... but I wonder why we need the Poisson here?)