Exam 6: Probability

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 club member owns a car or a house,or both?

You think you have a 90% chance of passing your next advanced financial accounting exam.This is an example of subjective approach to probability.

The probability of an event is the ____________________ of the probabilities of the simple events that constitute the event.

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} If 3 vehicles were involved,what proportion of accidents involved alcohol?

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. -If joint,marginal,and conditional probabilities are available,only joint probabilities can be used to determine whether two events are dependent or independent.

If P(A)= 0.25 and P(B)= 0.65,then P(A and B)is:

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 -{Equity Loan Rates Narrative} What is the most common interest rate?

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} Are being in the upper class and having a GPA over 3.0 related? Explain.

Mutual Fund Price An investor estimates that there is a 75% chance that a particular mutual fund's price will increase to $100 per share over the next three weeks,based on past data. -{Mutual Fund Price Narrative} Interpret the 75% probability.

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} Calculate P(A and O).

Certification Test A standard certification test was given at three locations.1,000 candidates took the test at location A,600 candidates at location B,and 400 candidates at location C.The percentages of candidates from locations A,B,and C who passed the test were 70%,68%,and 77%,respectively.One candidate is selected at random from among those who took the test. -{Certification Test Narrative} If the selected candidate passed the test,what is the probability that the candidate took the test at location B?

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} If the GPA of the student selected is over 3.0,what is the probability that the student is in the lower class?

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. P(B)

Construction Bids A construction company has submitted bids on two separate state contracts,A and B.The company feels that it has a 60% chance of winning contract A,and a 50% chance of winning contract B.Furthermore,the company believes that it has an 80% chance of winning contract A if it wins contract B. -{Construction Bids Narrative} What is the probability that the company will win neither contract?

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 allows us to compute conditional probabilities from other forms of probability.

Construction Bids A construction company has submitted bids on two separate state contracts,A and B.The company feels that it has a 60% chance of winning contract A,and a 50% chance of winning contract B.Furthermore,the company believes that it has an 80% chance of winning contract A if it wins contract B. -{Construction Bids Narrative} What is the probability that the company will win at least one of the two contracts?

Initial estimates of the probabilities of events are known as:

If P(A)= 0.20,P(B)= 0.30,and P(A and B)= 0,then A and B are:

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 conditional probability of event B given event A is denoted by P(A|B).

The outcomes of a sample space must be ____________________ and ____________________.