Final answer:
Without all necessary probabilities to use Bayes' theorem, we cannot directly calculate the probability that someone tests positive and is a chicken. We can approximate it using the complement of the false negative rate and the assumed probability of being a chicken, which results in an approximate likelihood of 0.575154%.
Step-by-step explanation:
To calculate the probability that someone tests positive and is a chicken, we would typically use Bayes' theorem. However, the question at hand does not provide all of the necessary probabilities to perform the full calculation. We know the false positive rate P(+|C') is 0.29%, the false negative rate P(-|C) is 0.87%, and the probability that individuals are not chickens P(C') is 99.42%. However, we do not have the overall probability of testing positive P(+), nor the probability that an individual is a chicken P(C), which is the complement of P(C') and can be calculated as 100% - 99.42% = 0.58%. Without these values, we cannot proceed with Bayes' theorem to find the probability that someone tests positive and is a chicken.
However, if all we need is the probability that an individual is a chicken and tests positive, assuming independence (which is not strictly correct due to the nature of conditional probabilities involved, but it's the closest we can get with the given information), we can calculate it as follows:
- P(C) = 0.58% (Probability of being a chicken)
- P(+|C) = 1 - P(-|C) = 1 - 0.87% = 99.13% (Probability of testing positive given that the individual is a chicken)
- P(C and +) = P(C) × P(+|C) = 0.58% × 99.13% = 0.575154%
This calculation represents an approximation and should be regarded with caution, as in real probability assessments related to tests and diagnoses, the dependencies of events are crucial.