The proportion of shoots which represents no aphids.

Question

3. Bayesian Inference – Updating Beliefs A medical test for a rare disease has the following characteristics: Sensitivity (true positive rate): 99% Specificity (true negative rate): 98% The disease occurs in 0.5% of the population. A patient receives a positive test result. Questions: a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.

Answer 1

Question

Chapter 5.2, Problem 46E

(a)

To determine

To find: The proportion of shoots which represents no aphids.

(b)

To determine

To explain: The probability of not observing any aphids with the obtained probability of part (a).

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