Question

Probability – Bayes Theorem

Orion India manufactures special heavy duty printers which have chips with unique embedded software targeted to different countries. This is a requirement because of the local laws of the importing country. 20% of their production is exported to America, 30 percent to China and the remaining to Britain. Occasionally, the wrong chips are installed in the printers and the local facility in the importing country will have to replace the wrong chip with the correct one. Based on the past data, it was found that 5% of the printers exported to America require replacement of the chip. The corresponding percentages for Britain and China are 10% and 15% respectively. The usual maintenance cost of each printer, on average is Rs. 1200. On the other hand, whenever replacement of the chip is required, it will cost an additional Rs. 3,000.

1. What is the joint probability that a printer is exported to Britain and it requires a chip replacement?
2. What is the probability that a printer requires a chip replacement?
3. What is the probability that a printer is exported to America, given that it required a chip replacement?
4. What should be the amount that the company should charge towards the warranty, if it wants to earn an additional 10% profit on the warranty related costs (including usual maintenance and chip replacement)?
5. In the financial year 2012-13, the company had incurred Rs. 3 million towards maintenance and chip replacement costs. How should this cost be allocated across the three different countries?

Answer 1

Problem 1: P(A printer is exported to Britain and it requires a chip replacement)

=P(It requires a chip replacement|A printer is exported to Britain)P(A printer is exported to Britain)

=0.10*(1-0.2-0.3)=0.05

Problem 2: P(A printer requires a chip replacement)

=P(Printer requires a chip replacement|A printer is exported to America)P(A printer is exported to America)+

P(Printer requires a chip replacement|A printer is exported to China)P(A printer is exported to China)+

P(Printer requires a chip replacement|A printer is exported to Britain)P(A printer is exported to Britain)

=0.05*0.2+0.15*0.30+0.10*(1-0.2-0.3)=0.105

Problem 3: P(A printer is exported to America|it required a chip replacement)

=[P(Printer requires a chip replacement|A printer is exported to America)P(A printer is exported to America)]/[P(A printer requires a chip replacement)]

=0.05*0.2/0.105=0.0952

Problem 4: Total expected Cost=1200+3000*P(A printer requires a chip replacement)=1200+3000*0.105=1515

Expected amount that the company should charge towards the warranty= 1515+1515*0.10=1666.5