An automobile insurance company divides customers into three risk categories: Good (G), Medium (M), and Poor (P). Assume the following distribution of customers: 70% are Good risks, 20% are Medium risks, and 10% are Poor risks. Assume that the probabilities of a customer filing an accident claim (C) in the course of a year are: 0.5% for Good, 1% for Medium, and 2.5% for Poor. A customer is chosen at random. a) What is the probability that the customer is a good risk and has filed a claim?b) What is the probability that the customer has filed a claim?c) Given that the customer has filed a claim, what is the probability that the customer is a good risk?

a) 0.035 = 3.5% probability that a customer is a good risk and has filed a claim.

b) 0.0395 = 3.95% probability that the customer has filed a claim.

c) 0.8861 = 88.61% probability that the customer is a good risk

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

In which

P(B|A) is the probability of event B happening, given that A happened.

is the probability of both A and B happening.

P(A) is the probability of A happening.

a) What is the probability that the customer is a good risk and has filed a claim?

70% are good risks.

Of those, 0.5% file a claim. So

0.035 = 3.5% probability that a customer is a good risk and has filed a claim.

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

0.5% of 70%(good risks)

1% of 20%(medium risks)

2.5% of 10%(poor risks). So

0.0395 = 3.95% probability that the customer has filed a claim.

c) Given that the customer has filed a claim, what is the probability that the customer is a good risk?

0.0395 = 3.95% probability that the customer has filed a claim means that

0.035 = 3.5% probability that a customer is a good risk and has filed a claim means that

Thus

0.8861 = 88.61% probability that the customer is a good risk

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

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step-by-step explanation:

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