Question

New car owners were asked to evaluate their experiences in buying a new car during the past 12 months. In the survey, the owners indicated they were most satisfied with their experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick. Assuming that each set of rankings is equally likely, what is the probability that owners ranked Subaru third?

Answer 1

Concepts and reason

The problem belongs to the concept of probability.

An experiment is an act or process of observation that leads to a single outcome that cannot be predicted with certainty

Outcome: An outcome is a particular result of experiment.

Sample space: The set of all the possible outcomes is called the sample space of the experiment and is usually denoted by S.

Event: An event is a subset of the sample space. An event occurs when one of the outcomes that belong to it occurs.

Probability: The probability is a number that reflects the chance or likelihood that a particular event will occur. This can be expressed as proportions that range from 0 to 1.

Fundamentals

The formula for finding the probability is,

$P = \frac{{{\rm{Favourable cases}}}}{{{\rm{Total number of cases}}}}$

Let define the events:

$\begin{array}{l}\\S = {\rm{Subaru}}\\\\H = {\rm{Honda}}\\\\B = {\rm{Buick}}\\\end{array}$

The sample space for orderings of the three dealers is,

$\left\{ \begin{array}{l}\\\left( {SHB} \right),\left( {SBH} \right)\\\\\left( {HSB} \right),\left( {HBS} \right)\\\\\left( {BSH} \right),\left( {BHS} \right)\\\end{array} \right\}$

Hence, there are 6 total possible ways to ordering three dealers.

Hence, there are 2 favorable cases for owners ranked Subaru third.

That is, $\left\{ {\left( {HBS} \right),\left( {BHS} \right)} \right\}$

The probability that owners ranked Subaru third is,

$\begin{array}{c}\\P = \frac{{{\rm{Favourable cases}}}}{{{\rm{Total number of cases}}}}\\\\ = \frac{2}{6}\\\end{array}$

Ans:

The probability that owners ranked Subaru third is $\frac{2}{6}.$