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

step-by-step explanation:

a and d

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form