$\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 $
$P\{X = i\} = \Large \frac{e^{\lambda}\lambda^{i}}{i!}$
$P\{X = i + 1\} = P(i) \times \Large \frac{\lambda}{i+1}$
$P\{X = 0\} = \Large \frac{e^{-2.3}\times 2.3^{0}}{0!} = 0.100$
$P\{X = 1\} = P(0) \times \Large \frac{2.3}{0+1} = 0.230$
$P\{X = 2\} = P(1) \times \Large \frac{2.3}{1+1} = 0.264$
$P\{X > 2\} = 1 - 0.100 - 0.230 - 0.264 = 0.406$