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

Name: Problem 35, Chapter 3: Statistics for Business and Economics
Uploaded: 2023-10-16T17:02:26-08:00
Duration: 4 min 22 s
Channel: Sanchit Jain
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

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.

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.

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.

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.

Transcript

00:01 According to the given question, a work crew for welding project is to be made of two craftsmen.

00:08 We need to continue here and four laborers.

00:14 So this is and four laborers.

00:20 We are going to continue here.

00:24 This value must be.

00:29 We need to continue here.

00:31 From total is five craftsmen.

00:38 We need to continue here.

00:41 This is six laborers.

00:47 We are going to continue here.

00:49 In the first case, any total different combinations that are possible.

01:05 Total possible total different combinations are five c2 multiplied by six c2.

01:15 This is sorry, this is four laborers.

01:18 So definitely we need to continue here with four laborers.

01:24 So definitely 64 we need to continue here.

01:29 So this is five factorial divided by five factorial divided by three factorial two factorial six factorial four factorial two factorial five four divided by two six multiplied by five divided by two.

01:50 This is canceled out.

01:52 So this is 150 total possible outcomes.

01:56 Now we need to continue here.

02:00 What would we ever be? so now we need to find a probability that brother of one of the craftsman is a laborer...

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