Poisson Distribution

Question

If 20 markers are drawn from a large number of markers in which 10% are red markers. What is the probability that the number of red markers drawn exceeds the expected number of red markers. (Use Poisson approximation and Binomial theorem). (Upto 3 decimal places)

Answer 1

P= 

 = np

Here n=20 and p=0.1

so , =2

Now probability the number of red markers drawn exceeds the expected number of red markers (K>2)

=1-P(k=0)-P(k=1)-P(k=2)

After putting values ,

P(k>2)=1-[(1+2+2)/e^-2]

=1-0.68

=0.32