geniusy_2006

ABC Auto Insurance classifies drivers as good, medium, or poor risks. Drivers who apply to them for insurance fall into these three groups in the proportions 30%, 50%, and 20%, respectively. The probability a “good” driver will have an accident is .01, the probability a “medium” risk driver will have an accident is .03, and the probability a “poor” driver will have an accident is .10. The company sells Mr. Brophy an insurance policy and he has an accident. What is the probability Mr. Brophy is:

a.

A “good” driver? (Round your answers to 3 decimal places.)

  Probability

b.

A “medium” risk driver? (Round your answers to 3 decimal places.)

  Probability

c.

A “poor” driver? (Round your answers to 3 decimal places.)

  Probability

There are four people being considered for the position of chief executive officer of Dalton Enterprises. Three of the applicants are over 60 years of age. Two are female, of which only one is over 60.

a.

What is the probability that a candidate is over 60 and female? (Round your answer to 2 decimal places.)

  Probability

b.

Given that the candidate is male, what is the probability he is less than 60? (Leave no cell blank, be certain to "0" when ever required.)

  Probability

c.

Given that the person is over 60, what is the probability the person is female? (Round your answer to 3 decimal places.)

  Probability

Reynolds Construction Company has agreed not to erect all “look-alike” homes in a new subdivision. Five exterior designs are offered to potential home buyers. The builder has standardized three interior plans that can be incorporated in any of the five exteriors.

How many different ways can the exterior and interior plans be offered to potential home buyers?

  Number of different ways

Four women’s college basketball teams are participating in a single-elimination holiday basketball tournament. If one team is favored in its semifinal match by odds of 1.95 to 1.05 and another squad is favored in its contest by odds of 2.75 to 1.25, what is the probability that:

a.

Both favored teams win their games? (Round your answer to 4 decimal places.)

  Probability

There are 100 employees at Kiddie Carts International. Fifty-seven of the employees are hourly workers, 40 are supervisors, 2 are secretaries, and the remaining employee is the president. Suppose an employee is selected:

a.

What is the probability the selected employee is an hourly worker? (Round your answer to 2 decimal places.)

  Probability

b.

What is the probability the selected employee is either an hourly worker or a supervisor? (Round your answer to 2 decimal places.)

  Probability

c.

Refer to part 2. Are these events mutually exclusive?

d.

What is the probability the selected employee is neither an hourly worker nor a supervisor? (Round your answer to 2 decimal places.)

  Probability

Refer to the following picture.

a.

What is the picture called?

b.

What rule of probability is illustrated?

c.

B represents the event of choosing a family that receives welfare payments. What does ?

The probability that the cause and the cure for all cancers will be discovered before the year 2020 is .20.

What viewpoint of probability does this statement illustrate?

The marketing research department at PepsiCo plans to survey teenagers about a newly developed soft drink. Each will be asked to compare it with his or her favorite soft drink. What is the experiment?

Solve the following:

a.

b.

   9P 3

c.

  7C 2

P(A1) = .20, P(A2) = .40, and P(A3) = .40.  P(B1|A1) = .25. P(B1|A2) = .05, and P(B1|A3) = .10.

Use Bayes' theorem to determine P(A3|B1). (Round your answer to 4 decimal places.)

  P(A3|B1)

Refer to the following table.

First Event

  Second Event

A1

A2

A3

Total

  B1

2    

2    

5    

9     

  B2

2    

4    

4    

10     

Total

4    

6    

9    

19     

a.

Determine P(A3). (Round your answer to 2 decimal places.)

  P(A3)

b.

Determine P(B2|A2). (Round your answer to 2 decimal places.)

  P(B2|A2)

c.

Determine P(B1 and A2). (Round your answer to 2 decimal places.)

  P(B1 and A2)

A local bank reports that 80% of its customers maintain a checking account, 60% have a savings account, and 50% have both.

1.

If a customer is chosen at random, what is the probability the customer has either a checking or a savings account? (Round your answer to 2 decimal places.)

  Probability

2.

If a customer is chosen at random, what is the probability the customer does not have either a checking or a savings account? (Round your answer to 2 decimal places.)

  Probability

A study of 201 advertising firms revealed their income after taxes:

  Income after Taxes

Number of Firms

  Under $1 million

104     

  $1 million to $20 million

59     

  $20 million or more

38     

a.

What is the probability an advertising firm selected at random has under $1 million in income after taxes? (Round your answer to 2 decimal places.)

  Probability

b-1.

What is the probability an advertising firm selected at random has either an income between $1 million and $20 million, or an income of $20 million or more? (Round your answer to 2 decimal places.)

  Probability

b-2.

What rule of probability was applied?

  Rule of probability

In each of the following cases, indicate whether classical, empirical, or subjective probability is used.

a.

A baseball player gets a hit in 34 out of 52 times at bat. The probability is .65 that he gets a hit in his next at bat.

b.

A seven-member committee of students is formed to study environmental issues. What is the likelihood that any one of the seven is randomly chosen as the spokesperson?

c.

You purchase one of 9 million tickets sold for Lotto Canada. What is the likelihood you will win the $2 million jackpot?

d.

The probability of an earthquake in northern California in the next 10 years is .73.