The Grapes of China
The Chinese wine industry has become very large. However, there are many quality control problems. Wine batches are systematically examined for alcohol content, total sugar, volatile acid, and other food additives. Suppose the Yantai Best Cellar Consulting Company claims that only 3% of all bottles are unqualified, or defective. Suppose six bottles of Yantai wine are selected at random.
a. What is the probability that none of the six bottles will be unqualified?
b. What is the probability that at least one of the bottles will be unqualified?
c. Suppose all six bottles are unqualified. Do you believe the company's claim? Justify your answer.