ueson 3 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] [? marks} {c} ve independent tosses of a fair coin yield Heads on the rst and last tosses. [3 marks} Part 2 From a survey of 4H] new IW'awasan Open University students chosen at random, it was discovered that 240 students have been to the library every day. Using this data, construct [a] 95% condence interval [1D marks} [b] 93% condence interval [10 marks} for the proportion of students who use the library every day Question 4 [a] The mean lifetime of 1m mobile phones in a sample is 1,500 hours and their standard deviation is 120 hours. [.1 is the mean lifeme of all the mobile phones produced. Perform a test of hypothesis that the sample comes from a population whose mean is 1,500 hours at 5% signicance level [it] marks} [b] Consider a random sample of 16 observations. The sample variance is 32.45. Construct a 53% condence interval for o2 [1t] marks}