105. The average density of pathogenic microorganisms in one cubic meter of air is 100. A sample of 2 dm $^{3}$ of air is taken. Find the probability that at least one microbe will be found in the sample.
Solution. Let the random variable $X$ be the number of pathogenic microorganisms found in 2 dm $^{3}$ of air. We adopt the hypothesis of a Poisson distribution of the number of microorganisms that can be detected in this volume. The expected value of $X$ is $\lambda=\frac{100}{1000} \cdot 2=0.2$. The probability that at least one microorganism will be detected in this volume is

$$
P=1-P_{0}=1-e^{-0.2}=1-0.819=0.181
$$