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In this question if we do simply probability calculation then it is 8/20 40%

but when I am appling poisson distribution then it is 40.4%.

why we are getting two different answers??

poison distribution is used when avg probability of some event is given while binomial distribution is used when exact probabilty is given...
thanks!!

but here I am using simple probability.
how you got probability 0.4

I m getting 33/40  i.e 0.825

Total flaws(>3)/Total number of sheets

No of sheets having flaws >= 3 / total no of sheets

8/20

40%

$\lambda =\large ( \frac{4}{20} \times 0 ) + ( \frac{3}{20} \times 1) + ( \frac{5}{20} \times 2 )+ ( \frac{2}{20} \times 3 ) + ( \frac{4}{20} \times 4) + (\frac{5}{20} \times 5 )+ ( \frac{1}{20} \times 6 ) = 2.3$

$P\{X = i\} = \Large \frac{e^{\lambda}\lambda^{i}}{i!}$

$P\{X = i + 1\} = P(i) \times \Large \frac{\lambda}{i+1}$

$P\{X = 0\} = \Large \frac{e^{-2.3}\times 2.3^{0}}{0!} = 0.100$

$P\{X = 1\} = P(0) \times \Large \frac{2.3}{0+1} = 0.230$

$P\{X = 2\} = P(1) \times \Large \frac{2.3}{1+1} = 0.264$

$P\{X > 2\} = 1 - 0.100 - 0.230 - 0.264 = 0.406$

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