Four different written driving tests are administered by the...

Name: Problem 26, Chapter 8: Applied Mathematics: For the Managerial, Life, and Social Sciences
Uploaded: 2026-06-15T03:43:57-08:00
Duration: 1 min 39 s
Channel: Nick Johnson
Description: Four different written driving tests are administered by the Motor Vehicle Department. One of these four tests is selected at random for each applicant for a driver's license. If a group consisting of two women and three men apply for a license, what is the probability that a. Exactly two of the five will take the same test? b. The two women will take the same test?

Four different written driving tests are administered by the Motor Vehicle Department. One of these four tests is selected at random for each applicant for a driver's license. If a group consisting of two women and three men apply for a license, what is the probability that a. Exactly two of the five will take the same test? b. The two women will take the same test?

Four different written driving tests are administered by the Motor Vehicle Department. One of these four tests is selected at random for each applicant for a driver's license. If a group consisting of two women and three men apply for a license, what is the probability that
a. Exactly two of the five will take the same test?
b. The two women will take the same test?

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Key Concepts

Random Selection and Equally Likely Outcomes

This concept refers to an experiment where each outcome has the same probability of occurring. In probability problems, it means that every option is chosen at random and no option is favored over another, which allows the use of uniform probability models.

Counting Principles and Combinatorial Analysis

This involves techniques such as the multiplication principle, combinations, and permutations that are used to count the number of ways events can occur, both for total possibilities and favorable outcomes. It is essential when calculating probabilities in scenarios where assignments or selections are made under various restrictions.

Probability as a Ratio of Favorable to Total Outcomes

This fundamental principle defines probability as the ratio between the number of favorable outcomes and the total number of outcomes in the sample space. It serves as the basic method for determining likelihoods once the counts of the possible event occurrences are established.

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