Following the lock-down in the UK due to Covid-19, some adults were suffering greatly from the isolation they had endured. The prospects of graduating with a decent degree and finding jobs in the future were concerns affecting a lot of young adults. John and Jane (JJ) are two young adults who were trying to work out the chances (probabilities) of events occurring based on historical information. They were both looking at various aspect of the near future job market. Question 1. Answer all parts John and Jane found that the probability of getting a job in a bank was calculated as 0.4. Assume that in this situation that you are only considering that either they have a bank job or not as the only two options. a) If we have a sample of 4 young adults going for a bank job. What is the probability that all four have the job? b) The probability of a randomly drawn individual getting the bank job is 0.4. What is the probability that two out of four applicants get a bank job? (20 marks) c) Jane suggests that they try throwing a fair coin. Joh says what about using a coin with two heads. You initially assign probabilities of 0.5 to each probability. The coin is then tossed three times with heads appearing each time (heads three times in a row). Use Bayes' theorem to work out the posterior probability that the coin is fair (30 marks)