The statistics department of the University of Fictonia predicts events of inter

Question

The statistics department of the University of Fictonia predicts events of interest in the country the following year, given certain data collected the current year. Here are some interesting statistics that have been collected:

In months that there is a plague, goat stampedes occur 33% of the time.

Plagues occured 4 out of the last 50 months.

On average, goat stampedes occured on 1 in every 5 months in which plagues did not occur.

A government auditor notices that the economics department always predicts that plagues occur when ever there are goat stampedes. How often is the statistics department correct? Is their prediction useful? Use Baye's theorem to solve the problem. Give all answers in decimal form, rounded to two signicant figures.

Explanation / Answer

Lets say probability of plague is P(A) = 4/50 = 2/25 = 0.08

Probability of Goat stampede lets say P(B) = ?

Goat stampede occurs when there is a plague P(B/A) = 1/3 = 0.333

Goat stampede occurs when there is no plagueP(B/A') = 1/5 = 0.20

so plagues occurs whenever there are govt stampedes that means it counts probability of plague occuring nearly equals to 1 so we have to check that probability by using bayes' theorem.

so probability of plague when Goat stampedes occures P(A/B)

= P(B/A) * P(A) / [P(B/A) P(A) + P(B/A')P(A') ]

= 1/3 * 2/25 / (1/3 * 2/25 + 1/5* 23/25)

= 0.003

so probability of that occuring is very low so economics department is totally wrong in this aspect.

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