An insurance company believes that 30% of drivers are careless. The probability that a careless driver...

An insurance company believes that 30% of drivers are careless. The probability that a careless driver will have an accident in any one-year period is 0.4. The probability that a careful driver will have an accident in any one-year period is 0.2. Find the probability that a driver will have an accident next year given that she has had an accident this year.

Expert Solution

P(accident )=P(careless and accident)+P(careful and accident)=0.3*0.4+0.7*0.2=0.26

therefore probability that a driver will have an accident next year given that she has had an accident this year

=P(accident next year|careless)*P(careless|accident)+P(accident next year|careful)*P(careful|accident)

=0.4*(0.3*0.4/0.26)+0.2*(0.7*0.2/0.26)=0.2923

orchestra answered 2 years ago

An insurance company insures two drivers, a safe driver and a risky driver. There is an...

An insurance company insures two drivers, a safe driver and a risky driver. There is an 8.5% chance the risky driver has an accident in a given year, in which case the cost (payout) to the company would be $1,000,000. The safe driver has a 1% chance of an accident, which costs the company $500,000. What is the expected payout (i.e., for accidents) to the company from insuring these two people?

In any given year, an insurance company believes the following: -0.6 of drivers are safe. -0.25...

In any given year, an insurance company believes the following: -0.6 of drivers are safe. -0.25 of safe drivers wear seatbelts -0.10 of unsafe drivers wear seatbelts -0.10 of safe drivers experience an accident in a year -0.20 of unsafe drivers experience an accident in a year -Given a driver experiences an accident, the driver has probability 0.01 they will be taken to the hospital if they were wearing a seatbelt -Given a driver experiences an accident, the driver has...

Accidents records by an auto insurance company suggest that the probability that an insured driver has...

Accidents records by an auto insurance company suggest that the probability that an insured driver has an accident is 0.05 If an accident occurs, the damage to the vehicle amounts to an average of $6240. What premium should the insurance company charge, in order to have an expected profit of $1000? On average the insurer should charge $.... (Round to 2 decimal points.)

The claims department at Wise Insurance Company believes that younger drivers have more accidents and, therefore,...

The claims department at Wise Insurance Company believes that younger drivers have more accidents and, therefore, should be charged higher insurance rates. Investigating a sample of 1,200 Wise policyholders revealed the following breakdown on whether a claim had been filed in the last 3 years and the age of the policyholder. Is it reasonable to conclude that there is a relationship between the age of the policyholder and whether or not the person filed a claim? Use the .05 significance...

A car insurance company suspects that the younger the driver is, the more reckless a driver...

A car insurance company suspects that the younger the driver is, the more reckless a driver he/she is. They take a survey and group their respondents based on age. Of 217 respondents between the ages of 16-25 (Group 1), 183 claimed to wear a seat belt at all times. Of 398 respondents who were 26+ years old (Group 2), 322 claimed to wear a seat belt at all times. Find a 95% confidence interval for the difference in proportions. Can...

car insurance company suspects that the younger the driver is, the more reckless a driver he/she...

car insurance company suspects that the younger the driver is, the more reckless a driver he/she is. They take a survey and group their respondents based on age. Of 217 respondents between the ages of 16-25 (Group 1), 183 claimed to wear a seat belt at all times. Of 398 respondents who were 26+ years old (Group 2), 322 claimed to wear a seat belt at all times. Find a 95% confidence interval for the difference in proportions. Can it...

Assume that on a typical Saturday evening, 5% of all drivers are intoxicated, and the probability that an intoxicated driver is involved in a car accident is 0.2.

Assume that on a typical Saturday evening, 5% of all drivers are intoxicated, and the probability that an intoxicated driver is involved in a car accident is 0.2. Police estimate that of all car trips on a Saturday evening end with an accident. (Please note 2% = 0.02) a. The number 0.2 corresponds to which probability? (A) Pr[car accident and intoxicated] (B) Pr[car accident or intoxicated] (C) Pr[car accidentſintoxicated] (D) Pr[car accident and not intoxicated] (E) Pr[intoxicated car accident] b. What is the probability a driver...

An insurance company collects data on seat-belt use among drivers in a country. Of 1300 drivers...

An insurance company collects data on seat-belt use among drivers in a country. Of 1300 drivers 30-39 years old, 22% said that they buckle up, where as 384 of 1200 drivers 55-64 years old said that they did. At the 10% significance level, do the data suggest that there is a difference in seat-belt use between drivers 30-39 years old and those 55-64? Calculate the test statistic z=

An insurance company collects data on seat-belt use among drivers in a country. Of 2000 drivers...

An insurance company collects data on seat-belt use among drivers in a country. Of 2000 drivers 30 -39 years old, 23% said that they buckle up, whereas 482 of 1800 drivers 55-64 years old said that they did. Find a 90% confidence interval for the difference between the proportions of seat-belt users for drivers in the age groups 30-39 years and 55-64 years. Construct a 90% confidence interval.

A manager for an insurance company believes that customers havethe following preferences for life insurance...

A manager for an insurance company believes that customers have the following preferences for life insurance products: 20% prefer Whole Life, 10% prefer Universal Life, and 70% prefer Life Annuities. The results of a survey of 200 customers were tabulated. Is it possible to refute the sales manager's claimed proportions of customers who prefer each product using the data?ProductNumberWhole94Universal68Annuities38Step 1 of 10: State the null and alternative hypothesis.Step 2 of 10: What does the null hypothesis indicate about the proportions...

Question