= Solution
For $n$ independent seeds the <probability> of at least one success is $1-(1-x)^n$. Requiring it to be at least $0.95$ gives $(1-x)^n\leq0.05$. For $0<x<1$, taking logarithms and dividing by the negative number $\log(1-x)$ reverses the inequality:
$$
n\geq\frac{\log0.05}{\log(1-x)}.
$$
The smallest permitted integer is therefore
$$
\boxed{n_{\min}=\left\lceil\frac{\log0.05}{\log(1-x)}\right\rceil}.
$$
The <ceiling function> is necessary because seeds are counted discretely. If $x=0$, no finite number suffices; if $x=1$, one seed suffices. The target is interpreted as at least a ninety-five percent chance, since exact equality may not be attainable with an integer count.
Back to article page
