Solving Poisson Distribution Homework for 50 Liters of Sediment

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Homework Statement


In one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 1.0. Suppose you are going to dig up and examine 50 liters of sediment at this site. Let r = 0, 1, 2, 3,… be a random variable that represents the number of prehistoric artifacts found in your 50 liters of sediment. Find the probability that you will find 1 or more artifacts in the 50 liters of sediment. Round your answer to the nearest ten thousandth.


Homework Equations


P(r) = (e^-lambda)*(lambda^r)/r!

The Attempt at a Solution


What is lambda? is it 10? or is it 10/50=0.2? i can't seem to figure it out.
i think r = 1
 
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λ is the number of artifacts in the 50 liters of sediment on average.

P(1) would be the probability you'd find exactly one artifact in the 50-liter sample, but the problem is asking you to find the probability of finding one or more. So you can't just set r=1 to get the answer you're looking for.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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