A taxicab moves between the airport, Hotel A, and Hotel B according to a Markov

Question

A taxicab moves between the airport, Hotel A, and Hotel B according to a Markov chain with transition probabilities:
P(airport -> A) = 0.7,
P(airport -> B) = 0.3,
P(A -> airport) = 0.9,
P(A -> B) = 0.1,
P(B -> airport) = 0.8,
P(B -> A) = 0.2.

a) If the taxicab starts at the airport, what is the probability that it will be at Hotel A two moves later?

b) Suppose the taxicab starts at the airport with probability 0.6 and starts at Hotel A and Hotel B with probability 0.2 each. What is the probability that it will be at Hotel B two moves later?

c) In the long run, what fraction of visits will the taxicab make to each of the three locations?

Explanation / Answer

a) probablity (E) =(P(airport -> B) = 0.3)*P(B -> A) = 0.2. =0.06 b)P (E) = case 1 starts at airport = P=0.6*0.7*0.1 =0.042 or case 2 starts at A = P = 0.2*0.7*0.3 + 0.2*0.1*0.1 =0.044 case 3 starts at B => P = 0.2*0.3*0.8 = 0.048 total = 0.042 +0.044 +0.048 = 0.134

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.