ABC Company prints text books. They use two modes of transportation to ship, rai

Question

ABC Company prints text books. They use two modes of transportation to ship, rail and truck. In the 20 years during which they have operated, only 2 percent of the packages carried by rail and only 3.5 percent of the packages carried by truck have been lost. The claims manager receives a call and is informed that a package containing text books sent by ABC Company has been lost. ABC sends 60% of the packages by rail and 40% by truck. The text books are indeed lost. What is the probability the text books were shipped by truck? Prove your answer statistically.

Explanation / Answer

P(truck | lost) = P(truck and lost)/P(lost)

= 0.4x0.035/(0.4x0.035 + 0.6x0.02)

= 0.5385

Probability that the text books were shipped by truck = 0.5385

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