If \(X\) measures the number of components that fail when tested, the specific probability function is given by
\begin{equation*}
f(x) = \binom{100}{x} 0.01^x 0.99^{100-x}.
\end{equation*}
The probability that at most one component fails is then given by
\begin{equation*}
F(1) = f(0) + f(1) = \binom{100}{0} 0.01^0 0.99^{100} + \binom{100}{1} 0.01^1 0.99^99 \\ = 0.99^{100} + 100 \cdot 0.01 \cdot 0.99^{99} = 0.99^{99}(0.99 + 100 \cdot 0.01 \\ = 0.99^{99} \cdot 1.99 \approx 0.73576.
\end{equation*}