Question Part 1:

Calculate the probabilities of the following events (a) Four independent tosses of a coin yielding a sequence {Head, Head, Tail, Head} (3 marks) (b) A pair of fair dice is thrown and the numbers displayed on the surface are equal (for example (1, 1) or (2, 2) and so on) (7 marks) (c) Five independent tosses of a fair coin yield Heads on the first and last tosses. (3 marks) Part 2: From a survey of 400 new WOU students chosen at random, it was discovered that 240 students have been to the library every day. Using this data, construct (a) 95% confidence interval (10 marks)

(b) 99% confidence interval (10 marks) for the proportion of students who use the library every day