Question 3.6 (6 marks) Recent gures suggest 28% of the emails sent on any given day are spam. You look at a library of spam emails and a library of legitimate (ie not spam) emails and nd that 11% of the spam emails contain the wor \"winner\" but only 1% of the legitimate emails do. a) Assuming your libraries are representative, estimate the probability that an email chosen uniformly at random from all the emails sent on a certain day is spam, given that it contains \"winner\". b) Assuming your answer to (a) is correct, what is the probability that there is at least one legitimate email amongst ten emails selected independently and uniformly at random from all the emails sent on a certain day that contain \"winner\