A detective is chasing a fugitive around three cities A, B, and C. Assume that t
ID: 3075248 • Letter: A
Question
A detective is chasing a fugitive around three cities A, B, and C. Assume that they move independently of each other. (Admittedly, this is an unrealistic assumption.) The detective's movements follow the transition matrix Po and the fugitive's movements follow the transition matrix PF: 0.2 0.5 0.31 A P0.3 0.3 0.4 B 0.1 0.4 0.5 C 0.3 0.6 0.11A PF 0.2 0.4 0.4B 0.3 0.3 04 C The detective will catch the fugitive if they are in the same city. Find the number of steps until this happens if the detective starts from city A and the fugitive from city B. Hint: Make a larger 2-part state definition chain with the location of each together. a. b. What is the probability that this occurs at city A?Explanation / Answer
1.
the probability of starting from state A and moved to state A is 0.2 (for detective )
the probability of starting from state A and moved to state B is 0.5 (for detective )
the probability of starting from state A and moved to state c is 0.3 (for detective )
the probability of starting from state B and moved to state A is 0.2 (for fugitive)
the probability of starting from state B and moved to state B is 0.4 (for fugitive)
the probability of starting from state B and moved to state C is 0.4 (for fugitive)
so the probability of getting caught is = P(A|A)*P(B|A) + P(A|B)*P(B|B)+ P(A|C)*P(B|C)
= (0.2*0.2)+(0.5*0.4)+(0.3*0.4)
=0.36
2. The probability of this occurs in city A is = P(A|A)*P(B|A)=(0.2*0.2)=0.04.