Please solve all parts

Question 1 18 pts A newly opened driving school is running a promotion to advertise their lessons to new drivers with learner permits. For each of the next 110 new drivers who receive their learner permit, a representative of the driving school invites them to ip a coin : "heads" means the new driver can take driving lessons for free, "tails" means the new driver will not receive any driving lessons. Let N be a random variable denoting the number of new drivers who take the driving lessons. 1. (3 marks) What is the probability distribution of N? 2. (2 marks) What is the expected value of N? The probability that a new driver will progress to passing their driving test without driving lessons is 0.2, while those who have taken the lessons would pass their driving test with probability 0.6. Let P be a random variable denoting the number out of all of the new drivers with learner permits who pass their driving test. 3. (6 marks) Derive an expression for El P l N ). (Hint: it may help to write P = PH + PT, where PH is the number who passed the driving test out of those who ipped "heads" (and hence received the lessons), and PT is the number who passed the driving test out of those who ipped I'tails\" (and missed out on the lessons). 4. (3 marks) Hence calculate El P). 5. (4 marks) After the promotion is completed you meet a new driver who has passed their driving test. What is the probability that they took the driving lessons