Please show the work and explanation for this question and use RMarkdown to show the code, and work. thank you

4. Recent terrorist threats have lead to an increase in airport security. It' a metal detector signals an alarm. then the passenger is stopped by airport security ofcers. Suppose that if a particular metal detector at an airport signals an alarm. there is a 30% chance that the cause is due to the passenger's jewellery. The detection of jewellery on one passenger is independent of the detection on any other passengers and the probability that a passenger is stopped due to jewelleryisthe same forall passengers. Total for Question 4: IE merits [a] What is the probability that of 4D passengers stopped, there will be exactly 2|} who are stopped [3 maria} due to jewellery? [b] What is the probability that of to passengers stopped. there will be more than 2|] who are [3 marlin} stopped due to jewellery? [c] On a given day. of the rst 4 people stoppedbythe metal detector. none were stopped because of [3 marks} their jewellery Given that no one has yet been stopped due to jewellery, what is the probability that within the rst It) people stopped, no one will be stopped due to jewellery. You should formulate this problem usingr conditional probabilities and the Geometric distribution [d] What is the probability that ll]th passenger stopped on a given day is the 4th one stopped due [3 marlin} to jewellery? [e] On a given day. the metal detector stops 1(1)!) people Suppose that every ll]th passenger stopped [4 maria} must undergo additional testing [usually a drug swab of their personal belongings}. That is. the ll]th, Ztlth, sou], ..., Billth and lllllllth passengers who are stopped will undergo additional testing. What is the probability that 5111 passenger stopped due to jewellery is also chosen to undergo additional testing? 1tierit'y your answer using simulation using rh inom