## How Does Your Auto Insurance Affect Probability?

Drivers are categorized by insurance companies based on their age, sex, marital status, driving history, and location. Insurance companies need to know what kinds of drivers are more likely to be involved in collisions since they are businesses that are seeking to turn a profit. They are more prone to file claims that will cost the insurance provider money. These predictions are made using probability by an actuary, a statistician, and the insurance company utilizes them to decide how much to charge specific individuals for insurance. Teenagers are subject to higher rates since they have been shown to pose a greater danger. How Does Your Auto Insurance Affect Probability?

**Examples 1 **

Seven red, six green, three orange, and four black marbles are included in a bucket. A random draw will be made for one marble. How likely is it that the stone is red?

**ANSWER: **Probability equals success total = number of red marbles total = seven red 20 𝑡𝑜𝑡𝑎𝑙 ≈ 35% The probability of the selected pebble being red is 35%.

**Example 2: **a query To better serve its workers, a manufacturer intends to reorganize the parking spots in its lot. According to the two-way chart below, the staff work three separate shifts and operate five distinct kinds of vehicles. A worker is chosen at random. What is the likelihood that a worker owns an SUV?

**Solution for Example 2:** Find the total number of workers, which is 246 using the Total columns. There are 91 SUV drivers in all, which can be found by looking in the SUV column. By generating a fraction, one may determine the likelihood. Probability = Success Total = # of employees that drive SUVs Total = 9 SUV drivers 246 Total 37% A 37% possibility exists that a worker drives an SUV.

Sixth Case 3 Due to a decrease in the number of night shift employees, the plant from Example 2 is considering shutting a portion of the parking lot at night. In light of their night shift employment, what is the likelihood that an employee rides a motorcycle? This is an illustration of conditional probability. Given that the individual works the night shift, the total number of persons who do so will serve as the denominator. The yellow cell in the table serves as a reminder of this. The number of workers who commute by motorbike and work the night shift makes up the fraction’s numerator. The green cell in the table serves as a reminder of this.

**Continued Example 3 SOLUTION**

The likelihood that a person drives a motorbike provided that they work the night shift may be expressed symbolically using letter symbols and a vertical line that stands for “given.” P(C|N) can be used to represent this. There is an 8% likelihood that a worker drives a motorbike if you are aware of their night shift schedule.

**Example 4:** a query Justin is doing a statistical study to see if sports cars are more likely to be in collisions than other kinds of vehicles in his community. He surveys 315 randomly chosen parents of high school kids, and the findings are shown in the table to the right. Does the data confirm Justin’s hypothesis that accidents involving sports vehicles are more common?

**Solution for Example 4: **Justin must evaluate P(A) and P(A|S), two probability. The likelihood of an accident for all kinds of cars in his study is P (A). We can determine the conditional probability P(A|S) if we limit our search to the set of sports vehicles. Justin’s argument was refuted since the odds of having an accident were the same for the group of sports vehicles as they were for everyone in the poll. In Justin’s poll, the proportion of persons who get into accidents is the same for both sports car drivers and the general population.

Events that are separate from one another

**Separate Events:** We refer to A and S as independent events based on the preceding example #4. If the occurrence of one event has no bearing on the likelihood of the other, then the two occurrences are independent. If A and B are considered independent, as they were in case #4, then If, then we may argue that occurrences A and B are related events.

**Use Case 5** The judge at a historic automobile event is Jhanvi. She is also putting up a report on the 135 vehicles on display. One hundred and seventy of the automobiles had manual transmissions, forty-three had air conditioning, thirteen had both, and thirty-five had neither. To feature on the report’s cover, a random automobile will be chosen. What is the likelihood that the automobile won’t have a manual gearbox but air conditioning? SOLUTION: Jhanvi presents some of her results using a Venn diagram. She allows M to stand in for manual-transmission automobiles and A to stand in for air-conditioned vehicles. She drew the aforementioned Venn diagrams. You’ll see that the sum of the figures in each area equals 135 vehicles. The 30 vehicles in the portion below that is tinted in dark blue do not have manual transmissions, but they do have air conditioning. The likelihood that the automobile on the report’s cover has air conditioning but no manual gearbox is 22%.

**Use Case 6** What is the conditional probability that a randomly chosen automobile is black provided that it has a tan interior using this Venn diagram, where the letter B is used if the car exterior is black and the letter T is used if the interior color is tan? SOLUTION: Look at the two separate areas that indicate the tan inner color in the circular. We utilize these figures to create the percentage that indicates the likelihood. There are 47 automobiles with tan interiors, and 8 of them have black interiors. Given that the inside of the automobile is tan, the conditional chance that it is black is around 17%.