Question

B5. (a) A factory makes 5 trucks per day, seven days per week. Each truck has probability 0.1 of being faulty, independently of any other trucks i) What is the probability that exactly two of the trucks made in one week are faulty? ii) What is the expected number of faulty trucks made per week? 5 marks (b) The workers at the factory are asked to keep making trucks until a faulty truck is made. Again each truck has probability 0.1 of being faulty, independently of any other trucks i) Give the name and parameters of the probability distribution of the number of trucks made? ii) What is the expected number of trucks made, including the faulty truck? 5 marks (c) Another factory makes buses. Over one five day period from Monday to Friday, it is known that exactly three faulty buses are made. A faulty bus has a uniform probability of being made on any given day of the five-day working week. i) Give the name and parameters of the probability distribution of the number of faulty buses being made on Monday? ii) What is the variance of the number of faulty buses being made on Monday? 5 marks (d) A third factory makes cars. Each car has a unique number plate. There are five cars and their five corresponding number plates. Ted has the job of putting the number plates on the cars. How- ever, he puts the number plates on the cars in a random order. i) Find the probability that he puts the number plates correctly on all the cars ii) Find the probability that he puts the first two number plates on the correct cars and puts each of the last three number plates on the wrong car ii Find the probability that he puts the number plates correctly on exactly two cars 5 marks

Answer 1

0.9) expel in b