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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)
asked in Probability by Active (1.3k points)   | 80 views

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P= {\displaystyle {\frac {\lambda ^{k}e^{-\lambda }}{k!}}}

\lambda = np

Here n=20 and p=0.1

so , \lambda=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

 

answered by Active (1.7k points)  
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