Question

1. Once tourists arrive in their hotel in Dublin, they mainly want to enjoy shopping on Grafton Street and a day at Dublin Zoo the next day. From survey data, whern tourists check in to their hotel in Dublin, 60% of tourists plan to go to Grafton Street the next day, 30% to Dublin Zoo, and only 10% stay at their hotel. When on Grafton Street, 50% return to Grafton Street the next day, 30% plan to go to Dublin Zoo the next day, and 20% stay in the hotel. Finally, when at Dublin Zoo. 30% return the next day, 30% go Grafton Street the next day, while 40% stay in their hotel the next day. (a) Construct a transition diagram, clearly labelling the probabilities, to represent this situation. [5 marks] [5 marks] will spend their final day in the hotel at the end of a 4-day trip. b) Construct a transition matrix to represent this situation (c) Starting from the hotel, what is the probability (in percentage) that a tourist [8 marks] (d) Determine the long-term probability that a tourist spends the final day of their long trip at Dublin Zoo. [14 marks]

Answer 1

a) Given thot Let the States op Markov Chain are States Meani At Dublin oo At ttotel in Dublin a) Transitiom diagam O 3 D.4

ib) Transt tiom Matsix: mext State 0.3 04 0 3 9-3 state Let , ПСП) psobability distibutiom oP t these Dlaces on the n-th da Staating rom the hotel 0 hotel ารู้ Co1 Pobabilty distaibutiom om th da

4- 0.3 04 0 3 3 o.936 0- 4638 0.3 0 365 4635 9.3 0 364 4634 -4635 ,19-3 อ. 2365 H 0 a365 ttence The e Probabi lity that a toorist spend thelx nal day the hotel om 4th day Is 0.9365 -tesm paobability distributiom SatisPies

0.3 04 0.3 0.3 。.ว 0.5 四, 3 .5 We have Q Co

[CD T(D Hence Raqed probabilityb. Thanking you