Write the solution both in terms of a Binomial random variab

Write the solution both in terms of a Binomial random variable as well as its approximation with a Poisson. Which of the two approaches is computationally easier and why?

While writing her Ph. D dissertation, a doctoral student makes a typo every 350 words. A typical page contains about 250 words. What is the probability that she will make at least 2 typos in 4 pages?

(Not necessary to compute the harder of the two, just write out the ingredients of the solution.)

Define the random variable, its distribution and the parameters of the distribution clearly before solving

Please show all details so that I may learn the process. Thank you.

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials

a typo every 350 words
A page contain 250 words, for 4 pages it is 1000
Mean rate of typo for 1000 words is = 1000/350 = 2.857

P( X < 2) = P(X=1) + P(X=0) +
= e^-2.857 * 0 ^ 1 / 1! + e^-2.857 * ^ 0 / 0! +   
= 0.2215
P( X > = 2 ) = 1 - P (X < 2) = 0.7785