A work crew for a building project is to be made up of 2...

Name: Problem 35, Chapter 3: Statistics for Business and Economics: Global Edition
Uploaded: 2021-12-24T15:37:44-08:00
Duration: 2 min 22 s
Channel: Christopher Stanley
Description: A work crew for a building project is to be made up of 2 craftsmen and 4 laborers selected from a total of 5 craftsmen and 6 laborers. a. How many different combinations are possible? b. The brother of one of the craftsmen is a laborer. If the crew is selected at random, what is the probability that both brothers will be selected? c. What is the probability that neither brother will be selected?

A work crew for a building project is to be made up of 2 craftsmen and 4 laborers selected from a total of 5 craftsmen and 6 laborers. a. How many different combinations are possible? b. The brother of one of the craftsmen is a laborer. If the crew is selected at random, what is the probability that both brothers will be selected? c. What is the probability that neither brother will be selected?

A work crew for a building project is to be made up of 2 craftsmen and 4 laborers selected from a total of 5 craftsmen and 6 laborers.
a. How many different combinations are possible?
b. The brother of one of the craftsmen is a laborer. If the crew is selected at random, what is the probability that both brothers will be selected?
c. What is the probability that neither brother will be selected?

Key Concepts

Multiplication Principle

The multiplication principle states that if there are several independent tasks to be performed, and each task can be done in a set number of ways, the total number of ways to perform all tasks is the product of the ways each individual task can be performed. This principle is essential when combining independent selections, such as choosing craftsmen and laborers separately.

Combinatorial Counting

This concept involves calculating the number of ways to select a subset of items from a larger set without regard to order. It typically employs the use of binomial coefficients, which are central to solving problems involving selections from groups, such as choosing members for a crew.

Probability Calculation

This principle is used to determine the likelihood of an event by dividing the number of favorable outcomes by the total number of possible outcomes. In problems involving selections, it requires careful counting of both the total possibilities and the scenarios that satisfy the given conditions.

Conditional Selection and Restrictions

In probability problems, additional conditions (like the inclusion or exclusion of specific individuals based on relationships or attributes) require modifying the counting process to address the restrictions. This ensures that the counts reflect only the outcomes that meet the defined criteria, which is crucial for accurate probability estimation under constraints.

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