M. Iqbal A. Ismail Sdn Bhd export ships which were manufactured from three different factories that are X, Y and Z with the proportions of 35%, 25% and 40% each respectively. Records show that the proportions of technical malfunctions of cars from each factory are 1%.
(a) Draw a tree diagram based on the information given
(b) What is the probability of technical malfunctions of ships?
(c) If a car is selected randomly and is turned to have a technical malfunction, calculate the probability if it was Z's ship.
(d) If a car is selected randomly and is turned to have a technical malfunction, calculate the probability if it was X's ship by using Bayes Theorem (25 marks)