Question

An automobile insurance company divides customers into three categories, good risks, medium risks, and poor risks. Assume that 78% of the customers are good risks, 20% are medium risks, and 2% are poor risks. Assume that during the course of a year, a good risk customer has probability 0.005 of filing an accident claim, a medium risk customer has probability 0.01, and a poor risk customer has probability 0.025. A customer is chosen at random. What is the probability that the customer has filed a claim? Round the answer to four decimal places.

Answer 1

Answer:

There is a 0.64% probability that the costumer has filed a claim.

Step-by-step explanation:

Probability:

What you want to happen is the desired outcome.

Everything that can happen iis the total outcomes.

The probability is the division of the number of possible outcomes by the number of total outcomes.

Our problem has these following probabilities:

-78% that a costumer is a good risk.

-20% that a costumer is a medium risk.

-2% that a costumer is a poor risk.

Also:

- 0.5% of a good risk costumer filling an accident claim

- 1% of a medium risk costumer filling an accident claim.

-2.5% of a poor risk costumer filling an accident claim.

The question is:

What is the probability that the customer has filed a claim?

$P = P_[1} + P_{2} + P_{3}$, in which:

-$P_{1}$ is the probability that a good risk costumer is chosen and files a claim. This probability is: the probability of a good risk costumer being chosen multiplied by the probability that a good risk costumer files a claim. So:

$P_[1} = 0.78*0.005 = 0.0039$

-$P_{2}$ is the probability that a medium risk costumer is chosen and files a claim. This probability is: the probability of a medium risk costumer being chosen multiplied by the probability that a medium risk costumer files a claim. So:

$P_[2} = 0.20*0.01 = 0.002$

-$P_{3}$ is the probability that a poor risk costumer is chosen and files a claim. This probability is: the probability of a poor risk costumer being chosen multiplied by the probability that a poor risk costumer files a claim. So:

$P_[3} = 0.02*0.025 = 0.0005$

$P = P_[1} + P_{2} + P_{3} = 0.0039 + 0.002 + 0.0005 = 0.0064$

There is a 0.64% probability that the costumer has filed a claim.