A service station owner sells Goodroad tires, which are ordered from a local tire distributor. The distributor receives tires from two plants, A and B. When the owner of the service station receives an order from the distributor, there is a .50 probability that the order consists of tires from plant A or plant B. However, the distributor will not tell the owner which plant the tires come from. The owner knows that 20% of all tires produced at plant A are defective, whereas only 10% of the tires produced at plant B are defective. 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 owner believes 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 finds that it is defective.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A service station owner sells Goodroad tires, which are ordered from a local tire distributor. The
distributor receives tires from two plants, A and B. When the owner of the service station receives an order from the distributor, there is a .50 probability that the order consists of tires from plant A
or plant B. However, the distributor will not tell the owner which plant the tires come from. The
owner knows that 20% of all tires produced at plant A are defective, whereas only 10% of the tires
produced at plant B are defective. 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 owner believes 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 finds that it is
defective.
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