Question 2 (6 marks)

A soft drink bottling company maintains records concerning the number of unacceptable bottles of soft

drink obtaining from the filling and capping machines. It is learned that 1% of the bottles from Machine I

is non-confirming and 2.5% of the bottles from Machine II is non-confirming. Half of the bottles are

filled by Machine I and the other half are filled by Machine II.

(a) Draw a well-labelled probability tree diagram with joint probabilities calculated to

illustrate this information. (3 marks)

(b) If a bottle is selected randomly, find the probability that the selected bottle

(i) is non-confirming; (1 marks)

(ii) is filled by Machine I and it is confirming; (1 marks)

(iii) is filled by Machine II given that it is non-confirming. (1 marks)