Answer to Question #304516 in Microeconomics for Shakil Uddin

Question

Problem 1:

What do understand by the terms prior and posterior probabilities in relation to Bayes’ theorem?

 

Problem 2:

The problem with this disease is that once the first symptoms are observed and the veterinarian contacted, it can take several days for tests to be conducted and the results to be obtained. During this time, the disease can spread to other farms. However it is possible to carry out a quick test by the farmer, which will correctly diagnose the disease 80% of the time. Unfortunately, the test is prone to give a false positive reading on 40% of occasions, i.e. the probability that the test will give a positive reading when in fact the disease is absent is 0.4.

1. Draw a probability tree diagram to show how the prior probabilities and the conditional outcomes of the test can be combined to give the posterior probabilities.

Answer 1

1)

Prior probability stands for that which is originally believed before a piece of new evidence is given.

On the other hand, Posterior probability takes the presented new information into account.

2)

The tree diagram is shown below

KEY

Prior probabilities

D- Represents positive diagnosis.

D¹- Represents negative diagnosis.

Posterior probabilities

P- Represents positive readings.

P¹- Represents negative readings.