[tex]\text{The formula of the Poisson distribution is the following:}\\P_v(n)=\frac{v^ne^{-v}}{n!}\\\text{Wherein the parameter } v=pN=0.01\times100=1\\\text{So the formula becomes:}\\P(n)=\frac{1}{e\times n!}\\\text{3 errors means either no error, one error, two errors one three errors}\\\text{So we will compute the probability for n = 0, 1, 2 and 3:}\\P(0)=\frac{1}{e},P(1)=\frac{1}{e},P(2)=\frac{1}{2e},P(3)=\frac{1}{6e}\\\text{Adding we get the probability to have less than 3 errors:}\\0.98[/tex]
