Question

In a discount store, 12% of the 100 cups in stock have some unnoticeable defect. What is the probability of buying 12 cups that don’t have any defect? And what is the probability of getting all 12 cups having a defect?

Answer 1

The probability of buying 12 cups without any defect is calculated using the hypergeometric distribution, while the probability of all 12 cups having a defect is zero as there are only 12 defective cups in stock.

Step-by-step explanation:

The question is about calculating the probability of selecting cups without defects and the probability of selecting defective cups from a stock. In a discount store, if 12% of the 100 cups in stock have some unnoticeable defect, then 88 cups don't have any defect and 12 cups have a defect.

Probability of buying 12 cups without any defect calculations is based on the hypergeometric distribution since the sampling is without replacement and involves two groups: defective and non-defective cups. To find the probability of buying 12 non-defective cups, we use the formula P(X = 0) where X is the number of defective cups in the sample of 12 cups:

P(X = 0) = [(C(12, 0) * C(88, 12)) / C(100, 12)]

Similarly, the probability of all 12 cups having a defect is also calculated using the hypergeometric distribution:

P(X = 12) = [(C(12, 12) * C(88, 0)) / C(100, 12)]

However, because there are only 12 defective cups in the stock, the probability of picking 12 defective cups is 0 since we cannot pick more defective cups than what is available.