Exam 6: Probability

Equity Loan Rates A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records. Interest Rate 0.0\% 6.5\% 7.0\% 7.5\% >7.5\% Probability 0.20 0.23 0.25 0.28 .04 -The union of events A and B is the event that occurs when either A or B or both occur.It is denoted as 'A or B'.

Equity Loan Rates A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records. Interest Rate 0.0\% 6.5\% 7.0\% 7.5\% >7.5\% Probability 0.20 0.23 0.25 0.28 .04 -If A and B are independent events with P(A)= .40 and P(B)= .50,then P(A and B)= .20.

Messenger Service Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries,service B has 30%,and service C has the remaining 10%.Their on-time rates are 80%,60%,and 40% respectively.Define event O as a service delivers a package on time. -{Messenger Service Narrative} If a package was delivered 40 minutes late,what is the probability that it was service B?

Business Majors Suppose 30% of business majors major in accounting.You take a random sample of 3 business majors. -{Business Majors Narrative} What is the chance that at least one majors in accounting?

Financial Consultants A Financial Consultant has classified his clients according to their gender and the composition of their investment portfolio (primarily bonds,primarily stocks,or a balanced mix of bonds and stocks).The proportions of clients falling into the various categories are shown in the following table: Portfolio Composition Gander Bonds Stocks Balanced Male 0.18 0.20 0.25 Female 0.12 0.10 0.15 One client is selected at random,and two events A and B are defined as follows: A: The client selected is male. B: The client selected has a balanced portfolio. -{Financial Consultants Narrative} Find the following probabilities: a. P(A|B) b. P(B|A)

The collection of all possible events is called

Is it possible to have two events for which P(A)= 0.40,P(B)= 0.50,and P(A or B)= 0.30? Explain.

Condo Sales and Interest Rates The probability that condo sales will increase in the next 6 months is estimated to be 0.30.The probability that the interest rates on condo loans will go up in the same period is estimated to be 0.75.The probability that condo sales or interest rates will go up during the next 6 months is estimated to be 0.90. -Bayes' Law says that P(A|B)= P(B|A)P(A).

In the scenario of Bayes' Law,P(A|B)is a(n)____________________ probability,while P(B|A)is a posterior probability.

A sample space of an experiment consists of the following outcomes: 1,2,3,4,and 5.Which of the following is a simple event?

When you multiply a first level branch with a second level branch on a probability tree you get a(n)____________________ probability.

Condo Sales and Interest Rates The probability that condo sales will increase in the next 6 months is estimated to be 0.30.The probability that the interest rates on condo loans will go up in the same period is estimated to be 0.75.The probability that condo sales or interest rates will go up during the next 6 months is estimated to be 0.90. -In problems where the joint probabilities are given,we can compute marginal probabilities by adding across rows and down columns.

Club Members A survey of a club's members indicates that 50% own a home,80% own a car,and 90% of the homeowners who subscribe also own a car. -{Club Members Narrative} What is the probability that a subscriber owns both a car and a house?

GPA and Class A college professor classifies his students according to their grade point average (GPA)and their class rank.GPA is on a 0.0-4.0 scale,and class rank is defined as the under class (freshmen and sophomores)and the upper class (juniors and seniors).One student is selected at random. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ GPA Class Under 2.0 2.0 - 3. 0 Over 3.0 Under 0.05 0.25 0.10 Upper 0.10 0.30 0.20 -{GPA and Class Narrative} What is the probability that the student is in the upper class and has GPA under 2.0?

Marital Status An insurance company has collected the following data on the gender and marital status of 570 customers. Marital Status Gender Single Married Divorced Male 50 250 30 Female 100 100 40 Suppose that a customer is selected at random. -{Marital Status Narrative} Develop the joint probability table.

Drunk Drivers Six hundred accidents that occurred on a Saturday night were analyzed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below: Number of Vehieles Involved Did aloholplay a role? 1 2 3 Totals Yes 75 125 50 250 Na 50 225 75 350 Totals 125 350 125 600 -{Drunk Drivers Narrative} What proportion of accidents involved alcohol or a single vehicle?

If P(B)= .7 and P(A|B)= .7,then P(A and B)= 0.

Which of the following statements is correct if the events A and B have nonzero probabilities?

Messenger Service Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries,service B has 30%,and service C has the remaining 10%.Their on-time rates are 80%,60%,and 40% respectively.Define event O as a service delivers a package on time. -{Messenger Service Narrative} If a package was delivered 40 minutes late,what is the probability that it was service C?

If A and B are mutually exclusive events,with P(A)= 0.20 and P(B)= 0.30,then the probability that both events will occur simultaneously is: