Entrance to a country can be denied for a number of reasons. When someone arrives by air, and their entry is denied, they get put into a detention hotel before deportation. TWhile in the hotel they can appeal against the deportation decision. If the appeal is accepted they will be allowed to enter the country, if it's rejected, they have one more chance for appeal before getting deported. If their second appeal is successful, they can leave the hotel and enter the country, but if this second appeal is unsuccessful again, they will be deported. The possible scenarios can be found in the table below: First appeal ' Second appeal Outcome Successful No second appeal Entrance allowed Rejected Successful Entrance allowed Rejected Rejected Deportation Historic data shows that 70% of people who end up in the detention hotel, are there because they made a minor mistake in the visa application, while 10% get put into the detention hotel because they lied in the visa application (and it's possible to prove it}, while 20% have missing documents. If a minor mistake was the reason behind the initial rejection, then each appeal has a 95% chance of being successful. However if the reason was a provable lie or missing documents, then an appeal gets rejected with probability 0.93. (6 marks) By conditioning on the events {Minor mistake AND First appeal was successful; Minor mistake AND First appeal was rejected; Lie/Missing document AND First appeal was successful; Lie/Missing document AND First appeal was rejected} find the probability that a randomly chosen person from the detention hotel is eventually allowed to enter the country