Question 1 (a) (b) Two students are enrolled in a statistics exam. Assume that the probability that student A passes the exam 1s 50%. and student B 90%. The event that student A passes the exam or not does not affect the performance of student B. (1) Compute the probability that at least one of the two students will pass the exam. (5 marks) (11) If at least one of the two students passes the exam, what 1s the probability that student A fails the exam? (5 marks) (111) If at least one of the two students passes the exam. what 1s the probability that student A passes the exam? (5 marks) Each day. the price of a particular stock can move randomly by step size of $1.5 units up with probability p. or 1 unit down with probability 1-p. Each day's movement 1s mndependent of one another. (1) Assuming that the stock started at $100. compute the probability that, after 50 days, the position of the stock 1s at least $110, assuming that p = 0.5. (10 marks) (11) Calculate the expected price after n days. expressing vour answer in p and q. where q=1-p. (p 1s not 0.5))