Exam 2: Introduction to Probability

The intersection of A and A^c is the entire sample space.

When the results of experimentation or historical data are used to assign probability values,the method used to assign probabilities is referred to as the

A medical research project examined the relationship between a subject's weight and recovery time from a surgical procedure,as shown in the table below. a.Use relative frequency to develop a joint probability table to show the marginal probabilities. b.What is the probability a patient will recover in fewer than 3 days? c.Given that recovery takes over 7 days,what is the probability the patient is overweight?

If P(A $\cup$ B)= P(A)+ P(B),then A and B are mutually exclusive.

To better track its patients,a hospital's neighborhood medical center has gathered this information. a.Develop a joint probability table.Include the marginal probabilities. b.Find the conditional probabilities: P(A|N),P(A|E),P(W|N),P(W|E),P(N|A),P(E|A),P(N|W),P(E|W)

Through a telephone survey,a low-interest bank credit card is offered to 400 households.The responses are as tabled. a.Develop a joint probability table and show the marginal probabilities.. b.What is the probability of a household whose income exceeds $40,000 and who rejects the offer? c.If income is < $40,000,what is the probability the offer will be accepted? d.If the offer is accepted,what is the probability that income exceeds $40,000?

If A and B are mutually exclusive events,then P(A|B)= 0.

Safety Insurance Company has compiled the following statistics.For any one year period: The percentage of Safety's policyholders in each category are: a.What is the probability that a randomly selected policyholder will have an accident within the next year? b.Given that a driver has an accident,what is the probability that the driver is a male over 25? c.Given that a driver has no accident,what is the probability the driver is a female? d.Does knowing the fact that a driver has had no accidents give us a great deal of information regarding the driver's sex?

Higbee Manufacturing Corp.has recently received 5 cases of a certain part from one of its suppliers.The defect rate for the parts is normally 5%,but the supplier has just notified Higbee that one of the cases shipped to them has been made on a misaligned machine that has a defect rate of 97%.So the plant manager selects a case at random and tests a part. a.What is the probability that the part is defective? b.Suppose the part is defective,what is the probability that this is from the case made on the misaligned machine? c.After finding that the first part was defective,suppose a second part from the case is tested.However,this part is found to be good.Using the revised probabilities from part (b)compute the new probability of these parts being from the defective case. d.Do you think you would obtain the same posterior probabilities as in part (c)if the first part was not found to be defective but the second part was? e.Suppose,because of other evidence,the plant manager was 80% certain this case was the one made on the misaligned machine.How would your answer to part (b)change?

P(A|B)= 1 - P(B|A)for all events A and B.

Two events that are mutually exclusive cannot be independent.

Super Cola sales breakdown as 80% regular soda and 20% diet soda.While 60% of the regular soda is purchased by men,only 30% of the diet soda is purchased by men.If a woman purchases Super Cola,what is the probability that it is a diet soda?

When assigning subjective probabilities,use experience,intuition,and any available data.