A government task force suspects that some manufacturing...

A government task force suspects that some manufacturing companies are in violation of federal pollution regulations with regard to dumping a certain type of product. Twenty firms are under suspicion but all cannot be inspected. Suppose that 3 of the firms are; in violation. (a) What is the probability that inspection of 5 firms finds no violations? (b) What is the probability that the plan above will find two violations?

A government task force suspects that some manufacturing companies are in violation of federal pollution regulations with regard to dumping a certain type of product. Twenty firms are under suspicion but all cannot be inspected. Suppose that 3 of the firms are; in violation.
(a) What is the probability that inspection of 5 firms finds no violations?
(b) What is the probability that the plan above will find two violations?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Sampling Without Replacement

In scenarios where items are drawn from a finite set and each item is not returned to the population after being selected, the probabilities of subsequent selections change. This concept is critical in understanding and applying the hypergeometric distribution, as the lack of replacement makes each draw dependent on the previous ones.

Hypergeometric Distribution

This probability distribution applies to scenarios where samples are drawn from a finite population without replacement, and there are only two types of outcomes, typically labeled as successes and failures. It is used to determine the probability of drawing a specific number of successes from the population, given the total number of successes available.

Combinatorial Analysis

This involves counting the number of ways events can occur using combinations. In the context of the hypergeometric distribution, combinatorial analysis is used to calculate the total number of ways to choose items from a population, as well as the number of favorable outcomes that meet the criteria of the problem.

Transcript

Please give Ace some feedback