A town with a population 10,000 has suffered an outbreak of dragon pox, with 3% of the population be

Kendrick Hampton

Kendrick Hampton

Answered question

2022-06-13

A town with a population 10,000 has suffered an outbreak of dragon pox, with 3% of the population being infected. There is a test to diagnose the disease. If you have the dragon pox, the test will correctly register positive 97% of the time and will yield a false negative 3% of the time. If you do not have the dragon pox the test will register that correctly 97% of the time and will yield a false positive 3% of the time. Given that you tested positive for the disease, what is the probability that you actually have dragon pox?

Answer & Explanation

pyphekam

pyphekam

Beginner2022-06-14Added 27 answers

Need Bayes Theorem.
Let A = event that you have the disease.
Let B = event that you tested positive.
Let ( A B ) = event that both of the events A and B occurred.
p ( A | B ) = p ( A B ) p ( B ) .
p ( A B ) can be calculated as chance of having disease × chance of getting a true positive.
p ( B ) can be calculated as the above chance
plus the chance of not having disease × chance of getting false positive.

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