Are based on the following table, which shows...

Are based on the following table, which shows crashworthiness ratings for several categories of motor vehicles. ${ }^{10}$ In all of these exercises, take $X$ as the crash-test rating of a small car, $Y$ as the crash-test rating for a small SUV, and so on, as shown in the table. $$\begin{array}{|r|c|c|c|c|c|}\hline & & {}{} {\text { Overall Frontal Crash Test Rating }} \\\hline &\begin{array}{c}\text { Number } \\\text { Tested }\end{array} & \begin{array}{c}3 \\(\text { Good })\end{array} & \begin{array}{c}2 \\\text { (Acceptable) }\end{array} & \begin{array}{c}1 \\\text {(Marginal) }\end{array} & \begin{array}{c}0 \\\text { (Poor) }\end{array} \\\hline \text { Small Cars, } X &16 & 1 & 11 & 2 & 2 \\\hline \text { Small SUVs, } Y & 10 & 1 & 4 & 4 & 1 \\\hline \text { MediumSUVs,} Z & 15 & 3 & 5 & 3 & 4 \\\hline \text { Passenger Vans, } U & 13 & 3 & 0 & 3 & 7 \\\hline \text { Midsize Cars, } V & 15 & 3 & 5 & 0 & 7 \\\hline \text { Large Cars, } W & 19 & 9 & 5 & 3&2 \\\hline\end{array}$$ You choose, at random, a small car and a midsize car. What is the probability that both will be rated at most $1 ?$

Are based on the following table, which shows crashworthiness ratings for several categories of motor vehicles. ${ }^{10}$ In all of these exercises, take $X$ as the crash-test rating of a small car, $Y$ as the crash-test rating for a small SUV, and so on, as shown in the table.
$$\begin{array}{|r|c|c|c|c|c|}\hline & & {}{} {\text { Overall Frontal Crash Test Rating }} \\\hline &\begin{array}{c}\text { Number } \\\text { Tested }\end{array} & \begin{array}{c}3 \\(\text { Good })\end{array} & \begin{array}{c}2 \\\text { (Acceptable) }\end{array} & \begin{array}{c}1 \\\text {(Marginal) }\end{array} & \begin{array}{c}0 \\\text { (Poor) }\end{array} \\\hline \text { Small Cars, } X &16 & 1 & 11 & 2 & 2 \\\hline \text { Small SUVs, } Y & 10 & 1 & 4 & 4 & 1 \\\hline \text { MediumSUVs,} Z & 15 & 3 & 5 & 3 & 4 \\\hline \text { Passenger Vans, } U & 13 & 3 & 0 & 3 & 7 \\\hline \text { Midsize Cars, } V & 15 & 3 & 5 & 0 & 7 \\\hline \text { Large Cars, } W & 19 & 9 & 5 & 3&2 \\\hline\end{array}$$
You choose, at random, a small car and a midsize car. What is the probability that both will be rated at most $1 ?$

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Key Concepts

Multiplication Rule

The multiplication rule in probability states that if two events are independent, the probability that both events occur is equal to the product of the probabilities of each individual event. This rule is applied to calculate the combined probability of selecting a small car and a midsize car, both meeting the specified rating criterion.

Relative Frequency

Relative frequency is the method of estimating probability based on the outcomes observed in data. When using the table, the probability for each type of vehicle is estimated by dividing the number of vehicles with ratings meeting the condition by the total number of vehicles tested in that category.

Probability

Probability is a measure of the likelihood of an event occurring, defined as the ratio of the number of favorable outcomes to the total number of outcomes. In the context of the problem, it involves counting the vehicles that meet the specified criteria from the table and comparing this count to the total number of vehicles in that category.

Independent Events

Independent events are events whose outcomes do not affect each other. In the problem, selecting one small car and one midsize car are independent choices, meaning the probability of both events occurring together is the product of the probability of each individual event.

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