Final answer:
The probability of a shipment containing a 10% spoilage rate being approved is calculated using the hypergeometric distribution, specifically by dividing the combinations of selecting 10 good packages from the non-spoiled ones by the combinations of selecting any 10 packages from the total.
Step-by-step explanation:
The student asked a question related to probability. Specifically, they want to know the probability of a shipment being approved for quality even though there is a 10% spoilage rate among the packages. In this case, samples are being taken without replacement, which means that the problem is an example of hypergeometric distribution rather than a binomial distribution.
To calculate the probability of all 10 packages passing the inspection despite a 10% spoilage rate, we need to recognize that there are 100 spoiled packages within the 1000-package shipment. If 10 packages are chosen at random for the inspection, the chance that none of the inspected packages are spoiled is equivalent to choosing 10 from the 900 good packages.
The probability calculation would be:
P(shipment being approved) = (Number of ways to choose 10 good packages from the 900 good ones) / (Number of ways to choose 10 packages from all 1000 packages)
Using combinational calculations:
P(shipment being approved) = C(900, 10) / C(1000, 10)
Where C(n, r) is the combination of n items taken r at a time.