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Probability helps us measure how likely an event is to occur. To calculate probability, we use the formula: \( P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). Here, we're trying to find the probability that a passenger car will roll over in a crash.
First, we sum the total number of crashes, both rolled over and not rolled over. This requires adding the number of rolled-over cars (83,600) to those that didn't roll over (5,127,400). The resulting total is 5,211,000 crashes.
Next, we place the number of rollover crashes (83,600) over the total (5,211,000) giving us the probability formula: \( P(\text{rollover}) = \frac{83,600}{5,211,000} \).

Event likelihood refers to how probable or likely an event is to happen. In our case, the event is a passenger car rolling over during a crash. To express this, we use probability.
After simplifying the probability formula for a rollover, we get \( 0.016 \) or 1.6%. This percentage represents how likely it is for a car to roll over in a crash.
Because 1.6% is a small number, it indicates that rollover events are quite rare among passenger car crashes. Thus, it is unlikely for a car to roll over when it crashes.

The process of simplifying fractions is crucial in probability to make the numbers easier to interpret. For the rollover probability: \( \frac{83,600}{5,211,000} \), we can simplify it.
We do this by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, simplifying directly to a decimal gives us \( 0.016 \).
Converting this decimal to a percentage involves multiplying by 100, which results in 1.6%. This simplified fraction tells us that only a small fraction of car crashes result in rollovers.

Understanding probability in context is essential for analysis. The calculated probability of 0.016, or 1.6%, tells us that the likelihood of a passenger car rollover in a crash is low.
When interpreting this number, consider it as for every 100 car crashes, roughly 1 to 2 are likely to involve a rollover.
Such a low probability means that while rollovers can happen, they are not a common outcome in car crashes.

Statistical analysis allows us to draw insights from data. In this exercise, we determined the probability of a rollover by analyzing car crash data. This involved:

• Summing event occurrences (rollovers and non-rollovers)
• Calculating the total number of events (crashes)
• Determining the probability \( \frac{\text{83,600}}{\text{5,211,000}} \rightarrow 0.016 \)

These steps are part of a broader process that helps us make informed decisions and predictions based on statistical data.
By applying such analysis, safety measures can be evaluated and improved to reduce the likelihood of rollover accidents in the future.