In a 400-page manuscript, there are 200 random misprints. Assume that these misp

Question

In a 400-page manuscript, there are 200 random misprints. Assume that these misprints are distributed following Poisson distribution. If a page is selected, find the probability that it has one misprint. How many pages in the manuscript are there with no misprints? If two pages are selected, find the probability that they have two misprints. If two pages are selected, find the probability that they have 0 misprints or one misprint. If four pages are selected, find the probability that they have at least 1 misprints.

Explanation / Answer

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
In a 400-page manuscript, there are 200 random misprints

a.
if a page is selected that probability that has one print
mean rate of misprint for if a page is slected = 200/400 = 1/2 = 0.5

P( X = 1 ) = e ^-0.5 * 0.5^1 / 1! = 0.3033

c.
if a two page is selected that probability that has two misprint
mean rate of misprint for if a 2 page is slected = 2*[200/400] = 2*1/2 = 1
P( X = 2 ) = e ^-1 * 1^2 / 2! = 0.1839

d.
P( X < = 1) = P(X=1) + P(X=0)
= e^-1 * 1 ^ 1 / 1! + e^-1 * 2 ^ 0 / 0!
= 0.7358

e.
if four page is selected that probability that has atleast 1 misprint
mean rate of misprint for if a 4 page is slected = 4*[200/400] = 4*1/2 = 2
P( X = 2 ) = e ^-1 * 1^2 / 2! = 0.1839

P( X < 1) = P(X=0)   
= e^-2 * 2 ^ 0 / 0!   
= 0.1353
P( X > = 1 ) = 1 - P (X < 1) = 0.8647

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