In 2003,25 % of all light vehicles sold (SUVs, pickups,...

In $2003,25 \%$ of all light vehicles sold (SUVs, pickups, passenger cars, and minivans) in the United States were SUVs, and $15 \%$ were pickups. Moreover, a randomly chosen vehicle sold that year was five times as likely to be a passenger car as a minivan. $^{37}$ Find the associated probability distribution.

Key Concepts

System of Equations

When given multiple pieces of information about probabilities, such as specific given percentages and relational ratios, a system of equations is used to solve for the unknown values. This involves combining the known probabilities and relative likelihoods with the total probability requirement to determine the complete probability distribution.

Relative Likelihood

Relative likelihood deals with the comparison of the probabilities of different events, often expressed as a ratio. In problems where one event is stated to be a multiple times more likely than another, such as one category being five times as likely as another, this concept is key for setting up the necessary proportional relationships and equations.

Total Probability Rule

The total probability rule states that the sum of the probabilities of all mutually exclusive events in a probability distribution must equal one. This is fundamental when solving for unknown probabilities in any scenario, ensuring that the model accurately reflects all potential outcomes.

Probability Distribution

A probability distribution assigns a probability to each possible outcome in a sample space. In problems involving categorical outcomes, each event, such as types of vehicles or other categories, is assigned a probability such that the sum of all probabilities is equal to one. This concept underlies the solution process by ensuring that all possible outcomes are accounted for properly.

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