In: Statistics and Probability
The maker of Tangerine automobiles has two assembly plants: the one in Metropolis producers 36% of the vehicles; and the one in Gotham produces the other 64% of the vehicles. They then all are shipped to a distribution site, where they undergo extensive quality tests. It seems that 85% of the vehicles from Metropolis pass the test; but only 75% of vehicles from Gotham pass the test.
a- What is the probability that a randomly chosen vehicle shipped to the distribution site will fail the quality test?
b- You see a shiny new Tangerine in your local auto dealership; so it must have passed the quality test. What is the probability that it was assembled in Gotham?