Question

For the Markov matrix [0.8 0.3 0.2 0.7 ] there is a steady state and the product of the final probabilities is (note columns sum to one).

At a courthouse every person visiting must pass through an explosives detector. The explosives detector is 90% accurate when detecting the presence of explosives on a person but suffers from a 5% false positive rate. Past studies have determined that the probability that a random person will bring explosives into the courthouse is 0.1%. If the detector indicates that a random person has concealed explosives, what is the true probability they have explosives?

Answer 1

Q1) The steady state satisfies

-----(1) where

Using matrix properties we have by (1)

The product of these probabilities is 0.06

Q2) Probability of Positive test is given by total probability theorem as

Required probability using Bayes theorem