Question

A lot contains 10 items of which 3 are defective. Three items are chosen from the lot at random one after another without replacement. Find the probability that all the three are defective.

Name: Problem 44, Chapter 21: Business Mathematics and Statistics
Uploaded: 2021-07-22T01:53:57-08:00
Duration: 1 min 42 s
Channel: Goutam Chand
Description: A lot contains 10 items of which 3 are defective. Three items are chosen from the lot at random one after another without replacement. Find the probability that all the three are defective.

   A lot contains 10 items of which 3 are defective. Three items are chosen from the lot at random one after another without replacement. Find the probability that all the three are defective.

Business Mathematics and Statistics

Dr. J K Das 2011 Edition

Chapter 21, Problem 44

Instant Answer

Solved by Expert Goutam Chand

07/22/2021

Step 1

We are asked to find the probability of getting three defective items one after another without replacement. This can be written as $P(A \cap A \cap A)$. Show more…

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A lot contains 10 items of which 3 are defective. Three items are chosen from the lot at random one after another without replacement. Find the probability that all the three are defective.

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Key Concepts

Combinatorial Analysis

This concept involves counting the number of ways to select items from a set, commonly using combinations. It is used to determine both the total number of possible selections and the specific number of favorable selections when the order does not matter.

Sampling Without Replacement

This concept refers to the process of drawing items from a finite set where each drawn item is not returned to the set, thereby changing the probabilities of subsequent selections. It is crucial for accurately computing probabilities in sequential selection problems.

Hypergeometric Distribution

This is the probability distribution that describes the likelihood of a given number of successes in draws from a finite population without replacement. It is especially useful in situations where the population contains a fixed number of defective or successful items.

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