Old jet airliners (e.g. Boeing 747s) often had four engines (rather than two engines, which is now more common) because older engines were less reliable than modern engines. (a) Consider an airliner with four engines each with a probability of failure on a single flight of 0.001. The plane needs at least three engines to operate for it to reach its destination. What is the probability that the plane does not reach its destination on a single flight? [3 marks] (b) If in a given year this type of airliner flew 10 million times, how many times on average would they fail to reach their destination given your answer to part (a)? [1 mark] (c) Now, consider an airliner with two engines each with the same probability of failure as in part (a), i.e. 0.001. The plane only needs a single engine to operate for it to reach its destination. What is the probability that the plane does not reach its destination on a single flight? Briefly comment on the answer in comparison to your answer for part (a). [3 marks] (d) Using trial and error or otherwise to what probability of failure (to 1 significant figure) does the engine in part (c) need to decrease to have the same level of safety as the airline in part (a)? [3 marks]