Select The Correct Answer.Brenda Is Choosing A Car Insurance Plan. Based On Her Driving History And The Traffic Where She Lives, Brenda Estimates That There Is A $20%$ Chance She Will Have A Car Collision This Year. In Each Plan, The
Introduction
When it comes to choosing a car insurance plan, understanding the probability of accidents is crucial. In this scenario, Brenda is deciding on a car insurance plan based on her driving history and the traffic conditions in her area. She estimates that there is a 20% chance she will have a car collision this year. In this article, we will delve into the concept of probability and how it applies to car insurance plans.
What is Probability?
Probability is a measure of the likelihood of an event occurring. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In Brenda's case, the probability of having a car collision this year is estimated to be 20%, which can be expressed as 0.2.
Types of Probability
There are two main types of probability: theoretical probability and experimental probability.
- Theoretical Probability: This type of probability is based on the number of favorable outcomes divided by the total number of possible outcomes. For example, if a coin has two sides, the probability of landing on heads is 1/2 or 0.5.
- Experimental Probability: This type of probability is based on the number of times an event occurs in a series of trials. For example, if you flip a coin 10 times and it lands on heads 5 times, the experimental probability of landing on heads is 5/10 or 0.5.
Applying Probability to Car Insurance Plans
In Brenda's case, the probability of having a car collision this year is estimated to be 20%. This means that there is a 20% chance that she will have a car collision this year. To calculate the expected number of car collisions, we can multiply the probability by the total number of drivers.
For example, if there are 100 drivers in Brenda's area, the expected number of car collisions would be:
100 drivers * 0.2 (probability of having a car collision) = 20 car collisions
Expected Value
The expected value is a measure of the average value of a random variable. In this case, the expected value is the average number of car collisions per driver.
To calculate the expected value, we can multiply the probability by the number of drivers and the cost of each car collision.
For example, if the cost of each car collision is $10,000 and there are 100 drivers, the expected value would be:
100 drivers * 0.2 (probability of having a car collision) * $10,000 (cost of each car collision) = $20,000
Choosing the Correct Car Insurance Plan
Based on Brenda's driving history and the traffic conditions in her area, she estimates that there is a 20% chance she will have a car collision this year. To choose the correct car insurance plan, she needs to consider the following factors:
- Premium: The cost of the car insurance plan.
- Coverage: The amount of coverage provided by the car insurance plan.
- Deductible: The amount that Brenda needs to pay out of pocket before the insurance company pays for damages.
- Maximum payout: The maximum amount that the insurance company will pay for damages.
Conclusion
In conclusion, understanding probability is crucial when choosing a car insurance plan. By considering the probability of accidents and the expected value, Brenda can make an informed decision about which car insurance plan to choose. Remember, the key to choosing the correct car insurance plan is to consider the probability of accidents, the expected value, and the factors mentioned above.
Frequently Asked Questions
Q: What is probability?
A: Probability is a measure of the likelihood of an event occurring. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Q: What are the two main types of probability?
A: The two main types of probability are theoretical probability and experimental probability.
Q: How do I calculate the expected value?
A: To calculate the expected value, you need to multiply the probability by the number of drivers and the cost of each car collision.
Q: What factors should I consider when choosing a car insurance plan?
A: You should consider the premium, coverage, deductible, and maximum payout when choosing a car insurance plan.
Q: What is the expected value in this scenario?
A: The expected value is the average number of car collisions per driver, which is calculated by multiplying the probability by the number of drivers and the cost of each car collision.
Q: How do I calculate the expected number of car collisions?
A: To calculate the expected number of car collisions, you need to multiply the probability by the total number of drivers.
Q: What is the probability of having a car collision this year?
A: The probability of having a car collision this year is estimated to be 20%.
Q: What is the cost of each car collision?
A: The cost of each car collision is $10,000.
Q: How many drivers are there in Brenda's area?
A: There are 100 drivers in Brenda's area.
Q: What is the expected value in this scenario?
A: The expected value is $20,000.
Q: What is the expected number of car collisions?
Q: What is probability?
A: Probability is a measure of the likelihood of an event occurring. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Q: What are the two main types of probability?
A: The two main types of probability are:
- Theoretical Probability: This type of probability is based on the number of favorable outcomes divided by the total number of possible outcomes.
- Experimental Probability: This type of probability is based on the number of times an event occurs in a series of trials.
Q: How do I calculate the expected value?
A: To calculate the expected value, you need to multiply the probability by the number of drivers and the cost of each car collision.
Q: What factors should I consider when choosing a car insurance plan?
A: You should consider the following factors when choosing a car insurance plan:
- Premium: The cost of the car insurance plan.
- Coverage: The amount of coverage provided by the car insurance plan.
- Deductible: The amount that you need to pay out of pocket before the insurance company pays for damages.
- Maximum payout: The maximum amount that the insurance company will pay for damages.
Q: What is the expected value in this scenario?
A: The expected value is the average number of car collisions per driver, which is calculated by multiplying the probability by the number of drivers and the cost of each car collision.
Q: How do I calculate the expected number of car collisions?
A: To calculate the expected number of car collisions, you need to multiply the probability by the total number of drivers.
Q: What is the probability of having a car collision this year?
A: The probability of having a car collision this year is estimated to be 20%.
Q: What is the cost of each car collision?
A: The cost of each car collision is $10,000.
Q: How many drivers are there in Brenda's area?
A: There are 100 drivers in Brenda's area.
Q: What is the expected value in this scenario?
A: The expected value is $20,000.
Q: What is the expected number of car collisions?
A: The expected number of car collisions is 20.
Q: How do I choose the correct car insurance plan?
A: To choose the correct car insurance plan, you need to consider the probability of accidents, the expected value, and the factors mentioned above.
Q: What is the difference between theoretical and experimental probability?
A: Theoretical probability is based on the number of favorable outcomes divided by the total number of possible outcomes, while experimental probability is based on the number of times an event occurs in a series of trials.
Q: How do I calculate the probability of an event?
A: To calculate the probability of an event, you need to divide the number of favorable outcomes by the total number of possible outcomes.
Q: What is the formula for calculating the expected value?
A: The formula for calculating the expected value is:
Expected Value = (Probability x Number of Drivers x Cost of Each Car Collision)
Q: How do I use the expected value to make a decision?
A: You can use the expected value to make a decision by comparing the expected value to the cost of the car insurance plan. If the expected value is greater than the cost, it may be worth purchasing the car insurance plan.
Q: What is the relationship between probability and expected value?
A: The probability and expected value are related in that the expected value is a measure of the average value of a random variable, while the probability is a measure of the likelihood of an event occurring.
Q: How do I calculate the probability of a car collision?
A: To calculate the probability of a car collision, you need to consider the number of car collisions that have occurred in the past and the total number of drivers.
Q: What is the formula for calculating the probability of a car collision?
A: The formula for calculating the probability of a car collision is:
Probability = (Number of Car Collisions / Total Number of Drivers)
Q: How do I use the probability of a car collision to make a decision?
A: You can use the probability of a car collision to make a decision by comparing the probability to the cost of the car insurance plan. If the probability is high, it may be worth purchasing the car insurance plan.