Q3; Three factories produce light bulbs to supply the market. Factory A produces 20%, 50% of the tools are produced in factories B and 30% in factory C. 2% of the bulbs produced in factory A, 1% of the bulbs produced in factory B and 3% of the bulbs produced in factory C are defective. A bulb is selected at random in the market and found to be defective. Hint: (This question is testing your knowledge on Bayes’ Theorem).

3.2.1 Write expressions to represent the probabilities that a bulb selected at random is from factory A, B and C respectively.

3.2.2 If P(D) is the probability that a defective bulb is selected, what are the conditional probabilities that a bulb is defective given that it is selected from factory A, B and C respectively.

3.2.3 Calculate that the conditional probability that the bulb was produced by factory B given that it is defective written as P(B|D).