Question 1. [10 Marks] You are lost on the planet of Skaro, where a species called Daleks live. Two thirds of the population on Skaro are interdimensional travellers, a species called Time Lords, who give a correct answer to a question with probability 3 / 4. The remaining one third of the population are Daleks. Answers from Time Lords to repeated questions are independent even if the question and the individual Time Lord are the same. In contrast, if you ask a Dalek a question, the answer is always false. Note: it is not possible to tell the difference between Time Lords and Daleks just by looking at them because, in each case, the image that you see is not a true likeness. (a) You ask a random passerby which species is superior, Daleks or Humans. This is Question I. The answer is Humans. What is the probability that this answer to Ques tion I is correct? (b) You ask the same passerby again and receive the same reply. This is Question [1. Show the probability that this answer to Question 11 is correct is 1/2. (c) You ask the same passerby again, and receive the same reply. This is Question 111. What is the probability that this answer to Question III is correct? (d) You ask for the fourth time, and received the answer Humans. This is Question IV. Show that the probability that the answer to Question IV is correct is 27/70. (e) Show that, had the answer to Question IV been Daleks instead, the probability that Humans is nevertheless the correct answer is 9/ 10