service station owner sells Goodroad tires, which are ordered from a localtire distributor. The distributor receives tires from two plants, A and B. When the ownerof the service station receives an order from the distributor, there is a .50 probability thatthe order consists of tires from plant A or plant B. However, the distributor will not tellthe owner which plant the tires come from. The owner knows that 20% of all tiresproduced at plant A are defective, whereas only 10% of the tires produced at plant B aredefective. When an order arrives at the station, the owner is allowed to inspect it briefly.The owner takes this opportunity to inspect one tire to see if it is defective. If the ownerbelieves the tire came from plant A, the order will be sent back. Using Bayes’ rule,determine the posterior probability that a tire is from plant A, given that the owner findsthat it is defective.
service station owner sells Goodroad tires, which are ordered from a localtire distributor. The distributor receives tires from two plants, A and B. When the ownerof the service station receives an order from the distributor, there is a .50 probability thatthe order consists of tires from plant A or plant B. However, the distributor will not tellthe owner which plant the tires come from. The owner knows that 20% of all tiresproduced at plant A are defective, whereas only 10% of the tires produced at plant B aredefective. When an order arrives at the station, the owner is allowed to inspect it briefly.The owner takes this opportunity to inspect one tire to see if it is defective. If the ownerbelieves the tire came from plant A, the order will be sent back. Using Bayes’ rule,determine the posterior probability that a tire is from plant A, given that the owner findsthat it is defective.
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