Four equally qualified people apply for two identical...

Four equally qualified people apply for two identical positions in a company. One and only one applicant is a member of a minority group. The positions are filled by choosing two of the applicants at random. a. List the possible outcomes for this experiment. b. Assign reasonable probabilities to the sample points. c. Find the probability that the applicant from the minority group is selected for a position.

Four equally qualified people apply for two identical positions in a company. One and only one applicant is a member of a minority group. The positions are filled by choosing two of the applicants at random.
a. List the possible outcomes for this experiment.
b. Assign reasonable probabilities to the sample points.
c. Find the probability that the applicant from the minority group is selected for a position.

Key Concepts

Sample Space

The sample space refers to the complete set of all possible outcomes for a random experiment. In probability, defining the sample space is crucial because it sets the framework for analyzing events. For experiments involving selection or combination, listing all unique outcomes helps in visualizing the problem and ensuring that every possibility is considered.

Equally Likely Outcomes

Assigning equally likely outcomes assumes that each outcome in the sample space has the same chance of occurring. This is often a simplifying assumption used in probability problems to make computations straightforward, such as when selections are made randomly without bias. Under this assumption, probabilities can be assigned uniformly, with each outcome's probability being the reciprocal of the total number of outcomes.

Combinatorial Analysis

Combinatorial analysis involves counting and enumerating the ways in which elements can be arranged or chosen from a set, typically using formulas such as combinations or permutations. This concept is applied when determining the total number of outcomes in a scenario where order may or may not matter. It is essential for problems where one must list or count the possible groups or arrangements, as it leads directly to calculating probabilities by counting favorable and total outcomes.

Event Probability Calculation

Event probability calculation is the process of determining the likelihood of a specific event occurring by comparing the number of favorable outcomes to the total number of outcomes in the sample space. This method, often based on the ratio of counts when outcomes are equally likely, is foundational to understanding and solving probability problems where one event's occurrence is assessed against all possible outcomes.

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