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Suppose that 30 percent of the bottles produced in a certain plant are defective

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Suppose that 30 percent of the bottles produced in a certain plant are defective. If a bottle is defective, the probability is 0.9 that an inspector will notice it and re- move it from the filling line. If a bottle is not defective, the probability is 0.2 that the inspector will think that it is defective and remove it from the filling line.

a. If a bottle is removed from the filling line, what is the probability that it is defective?

b. If a customer buys a bottle that has not been removed from the filling line, what is the probability that it is defective?