 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/18/b/solution

Let

A, B, C

denote the mutually exclusive supplier events and

D

the defective-bulb event. Their probabilities and conditional defect rates are

P (supplier) P (D ∣ supplier) A 1/5 α B 2/5 α /2 C 2/5 α /4.

These supplier events partition the possible bulbs. The following calculations use the law of total probability and Bayes' theorem with that partition.

 New to topics? Read the docs here!