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Chapter 5: Q1E (page 296)

In Example 5.4.7, with位=0.2 andp=0.1, compute the probability that we would detect at least two oocysts after filtering 100 liters of water.

Short Answer

Expert verified

The probability of detecting at least two oocysts after filtering 100 liters of water is 0.594.

Step by step solution

01

Given information

位 = 0.2,p = 0.1,t = 100

02

Compute the probability 

Let, X, be the number of oocysts in 100 liters of water.

X follows a Poisson distribution with mean p位t = (0.1 x 0.2 x 100) = 2, where, p = 0.1, 位 = 0.2 and t = 100

The probability of detecting at least two oocysts after filtering 100 liters of water

\[\begin{array}{c}P\left( {X \ge 2} \right) = 1 - P\left( {X \le 1} \right)\\ = 1 - 0.1353 - 0.2707\\ = 1 - 0.406\\ = 0.594\end{array}\]

(Referring to the table of Poisson probabilities on page number 857 for the answer)

Therefore, the probability of detecting at least two oocysts after filtering 100 liters of water is 0.594.

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