A shipment of chemicals arrives in 15 totes. Three of the...

Name: Problem 186, Chapter 3: Applied Statistics and Probability for Engineers
Uploaded: 2021-08-14T09:02:24-08:00
Duration: 4 min 57 s
Channel: Sonam Khatri
Description: A shipment of chemicals arrives in 15 totes. Three of the totes are selected at random without replacement for an inspection of purity. If two of the totes do not conform to purity requirements, what is the probability that at least one of the nonconforming totes is selected in the sample?

A shipment of chemicals arrives in 15 totes. Three of the totes are selected at random without replacement for an inspection of purity. If two of the totes do not conform to purity requirements, what is the probability that at least one of the nonconforming totes is selected in the sample?

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Key Concepts

Combinatorial Analysis

This concept involves counting the number of ways to choose items from a set without regard to order. It is foundational for determining the total number of possible outcomes in problems where selections are made, such as choosing items from a shipment.

Sampling Without Replacement

This concept means that once an item is selected from a finite population, it is not returned, altering the probabilities of subsequent selections. It is essential for accurately modeling scenarios where each selection affects the remaining options.

Complement Rule

This principle is used in probability to simplify calculations by finding the probability of the complementary event and subtracting it from one. It is especially useful when directly computing the probability of the desired event is complex.

Hypergeometric Distribution

This probability distribution applies to situations where samples are drawn without replacement from a finite population that contains a fixed number of successes and failures. It models the likelihood of a given number of successes in the sample, which is relevant when assessing the chance of selecting nonconforming items.

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