An insurance company classifies drivers as low risk and high...

An insurance company classifies drivers as low-risk and high-risk. Of those insured, 75% are low-risk and 25% are high-risk. After a study, the company finds that during a 1-year period, 4% of the low-risk drivers had an accident and 8% of the high-risk drivers had an accident. a) Find the probability that a randomly selected driver had an accident during the 1-year period and is a high-risk driver. b) Find the probability that a randomly selected driver had an accident during the 1-year period or is a low-risk driver. Example of a high-risk driver. c) What is the probability that a randomly selected driver who has had no accident during the 1-year period is a high-risk driver?

Transcript

00:01 An insurance company classifies their drivers as low risk and high risk.

00:14 Of those that were insured, 75 % were low risk and 25 % were high risk.

00:24 After a study, the company finds that during that one year period, 4 % of the low -risk drivers had an accident, and 8 % of the high -risk drivers had an accident.

00:43 So if 4 % of the low risk had an accident, then no accident accounted for 96 % of the low risk drivers, and no accident accounted for 92 % of the high risk drivers.

01:10 So for part a, we want to determine the probability that a randomly selected driver had an accident during the first year, and is high risk.

01:22 So probability of an accident and high risk.

01:33 So that means we are talking about these individuals.

01:38 So this is your compound probability, the probability of being high risk multiplied by the probability of having an accident, given that you knew they were high risk.

02:02 So it's going to be 0 .25 times 0 .08 or an overall probability of 0 .02.

02:17 For part b, we want to determine the probability that a randomly selected driver had an accident or they were low risk.

02:41 So anytime we're working with or we have to worry about whether the events are mutually exclusive or not.

02:47 So we're going to determine the probability of having an accident, plus we're going to find the probability of being low risk, and then if these events are not mutually exclusive, we're going to subtract out the probability of having an accident and being low risk.

03:19 So the probability of having an accident.

03:22 Well, we could be low risk and have an accident, so we could follow this path, or we could be high risk and have an accident.

03:50 Plus, the probability of being low risk.

03:56 The probability of being low risk is just right here, minus the probability of having an accident and low risk.

04:10 Well, accident and low risk is this right here.

04:21 So if we multiply out right here, we're going to get .03.

04:26 And here, we're going to get point zero.

04:29 0 .02.

04:36 And if we multiply these out, we'll get 0 .03...