A manufacturing firm has invested in a testing machine to improve the quality of its output. The defective rate of their output has been 2% in the past. The testing machine is however not perfect and it thus rejects some of the defective outputs and allows some of the defective outputs to be passed as up to standard. The conditional probability of an output being rejected given that it is not defective is 0.01 and the conditional probability of an output not being rejected given that it is defective is 0.003.
i) What is the probability of an output being defective and not being rejected?
ii) What is the probability of an output not being rejected and not being defective?
iii) What is the probability of an output, which has not been rejected, being defective?
iv) The firm produces on average 1,000,000 parts per year. Each defective part sold costs the firm RM 15. A part, which is defective and is rejected, costs the firm RM 5. What is the annual cost to the firm of rejected and other defective parts?