Question 1: Calculation Total Quality Management (10 marks)

In a workshop, three robots, Q, R and S, are employed to make chairs

Robot Q makes 25% of the chairs

Robot R makes 45% of the chairs

The remaining chairs are made by Robot S

Evidence has shown that 2 percent of the chairs made by robot Q are defective, 3 percent of the chairs made by robot R, and 5 percent of the chairs made by robot S are defective

(a) Construct a tree diagram that illustrates all possible outcomes and probabilities (5 marks)

A chair is randomly selected.

(b) What is the probability that the chair that robot Q made is defective (1 marks)

(c) What is the probability of findings a broken chair (2 marks)

(d) Given that a chair is defective, what is the probability that it was not made by robot R (2 marks)