The probability that there is a misprint on a single page of a book?

Question

The probability that there is a misprint on a single page of a book
is 0.02. Use the Poisson approximation to the binomial to find the
probability that there are fewer than 5 misprints in a book with 300
pages.

Answer 1

P =(e^(-np))(n p^k) / k!

where:
e = the base of the natural logarithms;
n = the number of opportunities for event x to occur;
k = the number of times that event x occurs or is stipulated to occur; and
p = the probability that event x will occur on any particular occasion;

To find probability that there are fewer than 5 misprints in a book with 300 pages,
n = 300
p = 0.02
k < 5
P =sum (e^(-np))(n p^k) / k!
P = (e^(-300x0.02))(300x0.02^4) / 4!
+(e^(-300x0.02))(300x0.02^3) / 3!
+(e^(-300x0.02))(300x0.02^2) / 2!
+(e^(-300x0.02))(300x0.02^1) / 1!
+(e^(-300x0.02))(300x0.02^0) / 0!

P = 0.7586