Complete Question
The complete question is shown on the first uploaded image
Answer:
The probability is [tex]P(X \ge 1 ) = 0.003996[/tex]
Given that the probability is less than 0.05 , it means that it is low enough so that further testing of the individual samples is rarely necessary
Step-by-step explanation:
From the question we are told that
The probability of finding bacteria in a public swimming area is p = 0.002
Generally the probability of not finding bacteria in a public swimming area is mathematically represented as
[tex]q = 1- p[/tex]
=> [tex]q = 1- 0.002[/tex]
=> [tex]q =0.998[/tex]
Generally the the probability that a combined sample from public swimming areas will reveal the presence of bacteria is equivalent to the probability that at least one of the sample will reveal the presence of bacteria and this is mathematically represented as
[tex]P(X \ge 1 ) = 1 - P(X')[/tex]
Here [tex]P(X')[/tex] means that none of the 2 sample have bacteria which is mathematically represented as
[tex]P(X') = q^2[/tex]
Here 2 signifies that we are considering two samples
So
[tex]P(X') = 0.998^2[/tex]
[tex]P(X') = 0.996004[/tex]
So
[tex]P(X \ge 1 ) = 1 - 0.996004[/tex]
=> [tex]P(X \ge 1 ) = 0.003996[/tex]
