ABC Company prints text books.They use two models of transportation to ship, rai
ID: 3231574 • Letter: A
Question
ABC Company prints text books.They use two models 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 package 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).
*** Please show steps and work on how to solve problem; also state what formula or theory used to work it***
Explanation / Answer
According to Baye's law P(A | B) = P(A and B)/ P(B)
Here, we need to find P(text books were shipped by truck | text books are lost)
P(text books were shipped by truck | text books are lost) = P(testbooks were shipped by truck and are lost)/P(text books are lost)
= 0.035x0.4/(0.035x0.4 + 0.02x0.6)
= 0.5385