Mr. Andrews, a grape merchant, inquires about a certain wine that he tastes at a party. The host tells him that from a total of ten bottles of that wine, six came from the north vineyard and four came from the south vineyard. From this information, the merchant concludes that he should visit the north vineyard for a sample of the grapes. Later, he discovers that the wine in question came from a bottle labeled Classic Reserve, and 30 of 100 barrels of north vineyard wine were bottled with that label, while 130 of 200 barrels of south vineyard wine were bottled with that label. Given this new information, what is the probability that the wine came from the north vineyard?
Mr. Andrews, a grape merchant, inquires about a certain wine that he tastes at a party. The host tells him that from a total of ten bottles of that wine, six came from the north vineyard and four came from the south vineyard. From this information, the merchant concludes that he should visit the north vineyard for a sample of the grapes. Later, he discovers that the wine in question came from a bottle labeled Classic Reserve, and 30 of 100 barrels of north vineyard wine were bottled with that label, while 130 of 200 barrels of south vineyard wine were bottled with that label. Given this new information, what is the probability that the wine came from the north vineyard? (Hint: For this exercise, use Bayes's theorem.)
Let's event represents that the vine comes from north and event represents that the vine comes from south. It is given that 6 out of 10 bottle are from north so and 4 out of 10 bottles are from south so .
Let's event L represents that the bottle is labelled. It is given that labelled bottles from north is 30 out of 100, that means the probability of L given is ratio of 30 to 100.
Similarly, the ratio of 130 to 200 will give the probability of L given .
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