Question

In Exercises 25–32, find the probability and answer the questions.. Car Rollovers In a recent year in the United States, 83,600 passenger cars rolled over when they crashed, and 5,127,400 passenger cars did not roll over when they crashed. Find the probability that a randomly selected passenger car crash results in a rollover. Is it unlikely for a car to roll over in a crash?

Short answer

The probability that a car will rollover in a crash is equal to 0.02.

Yes, it is unlikely for a car to rollover in a crash.

Step-by-step solution

Given information

It is given that in a year, the number of passenger cars that rolled over in a crash is equal to 83,600.

The number of cars that did not rollover is equal to 5,127,400.

Describe the probability

Theprobability of an event is the number of favorable outcomes of an event upon the total number of outcomes.

Mathematically,

$P\left(A\right)=\frac{\text{Number}\text{of}\text{favourable}\text{outcomes}\text{of}\text{A}}{\text{Total}\text{number}\text{of}\text{outcomes}}$

Calculating the probability value

The total number of car crashes is the sum of the number of cars that rolled over and the number that did not rollover.

It is calculated as follows:

$$\begin{gathered} \text{Total}\text{number}\text{of}\text{car}\text{crashes}=83600+5127400 \\ =5211000 \end{gathered}$$

The number of cars that rolled over = 83600.

Let E be the event of selecting a car crash resulting in a rollover.

The probability of E is calculated as follows:

$$\begin{gathered} P\left(E\right)=\frac{\text{Number}\text{of}\text{cars}\text{that}\text{got}\text{rolled}\text{over}}{\text{Total}\text{number}\text{of}\text{car}\text{crashes}} \\ =\frac{83600}{5211000} \\ =0.0160 \end{gathered}$$

Therefore, the probability of selecting a car crash resulting in a rollover is equal to 0.0160.

Examining the event as rare

An event is unusual if the chance of occurrence for an event is lesser than 0.05.

It can be said that there is a 0.0160 chance of a car getting rolled over in a crash. As the probability value is considerably low, it can be said that it is unlikely for a car crash to result in a rollover.