Answer
Probably no, $0.0211$.
Work Step by Step
By using the complement rule:
P(at least one positive)=1−P(no positive)=$1−(1−\frac{213}{100,000})^{10}=1−(\frac{99,787}{100,000})^{10}≈0.0211$.
This is very close to 0, therefore the combined test samples probably won't be positive.