Question 1 In a 400page manuscript there are 100 random misp

Question 1: In a 400-page manuscript, there are 100 random misprints. Assume that these misprints are distributed following Poisson distribution.

a) If a page is selected, find the probability that it has one misprint.

b) How many pages in the manuscript are there with no misprints?

c) If two pages are selected, find the probability that they have two misprints.

d) If two pages are selected, find the probability that they have 0 misprints or one misprint.

a) If a page is selected, find the probability that it has one misprint.

Given X follows Poisson distribution with mean=100/400 =0.25

P(X=x)=(0.25^x)*exp(-0.25)/x! for x=0,1,2,...

So the probability is

P(X=1) =(0.25^1)*exp(-0.25)/1=0.1947002

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b) How many pages in the manuscript are there with no misprints?

P(X=0) =(0.25^0)*exp(-0.25)/1=0.7788008

So 0.7788008*400 =311.5203 pages

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c) If two pages are selected, find the probability that they have two misprints.

P(X=2) =(0.25^2)*exp(-0.25)/2 =0.02433752

So the probability is 0.02433752*0.02433752 =0.0005923149

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d) If two pages are selected, find the probability that they have 0 misprints or one misprint.

P( have 0 misprints or one misprint) =1-P(they have two misprints)

=1-0.0005923149 =0.9994077