M a r k e t S h a r e : L i g h t V e h i c l e s I...

M a r k e t ~ S h a r e : ~ L i g h t ~ V e h i c l e s ~ I n ~ $2000,15 \%$ of all light vehi- cles (SUVs, pickups, passenger cars, and minivans) sold in the United States were pickups and $55 \%$ were passenger cars. Moreover, a randomly chosen vehicle sold that year was twice as likely to be an SUV as a minivan. ${ }^{30}$ Find the associated probability distribution.

M a r k e t ~ S h a r e : ~ L i g h t ~ V e h i c l e s ~ I n ~ $2000,15 \%$ of all light vehi-
cles (SUVs, pickups, passenger cars, and minivans) sold in the United States were pickups and $55 \%$ were passenger cars. Moreover, a randomly chosen vehicle sold that year was twice as likely to be an SUV as a minivan. ${ }^{30}$ Find the associated probability distribution.

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Key Concepts

Probability Distribution

A probability distribution is a function that assigns a probability to each possible outcome in a sample space. In problems involving categorization, it describes the likelihood of each specific event occurring such that the sum of all probabilities equals 1, ensuring a complete representation of all potential outcomes.

Using Ratio and Proportional Relationships

When one event is stated as being a multiple (such as twice) as likely as another, this introduces a ratio relationship between their probabilities. This concept allows you to set up proportional equations that relate the unknown probabilities, facilitating the calculation of specific values within a probability distribution.

Normalization of Probabilities

Normalization is the process of ensuring that all calculated probability values add up to 1 (or 100% when expressed as percentages). In problems where partial percentages or ratios are given, normalization is necessary to distribute the remaining probability appropriately among the remaining outcomes.

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