Question: Metal fatigue causes cracks to appear on the skin of older aircraft. Assume that it is reasonable to model the number of cracks appearing on a \(1 \mathrm{~m}^{2}\) surface of planes of a certain model and vintage as Poisson with mean \(\lambda=.03\).

1. If \(1 \mathrm{~m}^{2}\) is inspected, assess the probability that at least one crack is present on that surface.
2. If \(10 \mathrm{~m}^{2}\) are inspected, assess the probability that at least one crack (total) is present.
3. If ten areas, each of size \(1 \mathrm{~m}^{2}\), are inspected, assess the probability that exactly one of these has cracks.

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