Exam 6: Probability

NARRBEGIN: College Professorship College Professorship A Ph.D. graduate has applied for a job with two colleges: A and B. The graduate feels that she has a 60% chance of receiving an offer from college A and a 50% chance of receiving an offer from college B. If she receives an offer from college B, she believes that she has an 80% chance of receiving an offer from college A. Let A = receiving an offer from college A, and let B = receiving an offer from college B.NARREND -Suppose A and B are two mutually exclusive events for which P(A) = 0.30 and P(B) = 0.40. a.Find P(A and B). b.Find P(A or B). c.Are A and B independent events? Explain using probabilities.

If P(A and B) = 1, then A and B must be mutually exclusive.

NARRBEGIN: Mutual Fund Price 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 past data.NARREND -{Mutual Fund Price Narrative} Interpret the 75% probability.

The collection of all the possible outcomes of a random experiment is called a sample space.

The outcomes of a sample space must be ____________________, which means that all possible outcomes must be included.

NARRBEGIN: Club Members 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.NARREND -{Club Members Narrative} What is the probability that a club member owns neither a car nor a house?

Suppose P(A) = 0.30. The probability of the complement of A is:

Which of the following statements is always correct?

NARRBEGIN: Messenger Service 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.NARREND -{Messenger Service Narrative} Calculate P(C and O).

NARRBEGIN: Equity Loan Rates 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 NARREND -{Equity Loan Rates Narrative} What approach was used in estimating the probabilities for the interest rates?

NARRBEGIN: Financial Consultants 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 Gender Bonds Stecks 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.NARREND -{Financial Consultants Narrative} Find the following probabilities: a.P(A|B) b.P(B|A)

Which of the following is an approach to assigning probabilities?

If A and B are mutually exclusive events with P(A) = 0.30 and P(B) = 0.40, then P(A or B) is:

The second set of branches of a probability tree represent ____________________ probabilities.

Prior probabilities can be calculated using the multiplication rule for mutually exclusive events.

Posterior probability of an event is the revised probability of the event after new information is available.

NARRBEGIN: GPA and Class 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. 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 NARREND -{GPA and Class Narrative} What is the probability that the student is in the upper class?

If the outcome of event A is not affected by event B, then events A and B are said to be

In problems where the joint probabilities are given, we can compute marginal probabilities by adding across rows and down columns.

NARRBEGIN: College Professorship College Professorship A Ph.D. graduate has applied for a job with two colleges: A and B. The graduate feels that she has a 60% chance of receiving an offer from college A and a 50% chance of receiving an offer from college B. If she receives an offer from college B, she believes that she has an 80% chance of receiving an offer from college A. Let A = receiving an offer from college A, and let B = receiving an offer from college B.NARREND -Suppose P(A) = 0.30, P(B) = 0.50, and P(B|A) = 0.60. a.Find P(A and B). b.Find P(A or B). c.Find P(A|B).