Exam 6: Probability

NARRBEGIN: Marital Status Marital Status An insurance company has collected the following data on the gender and marital status of 600 customers. Marital Status Gender Single Maried Divorced Male 50 250 30 Female 100 100 40 Suppose that a customer is selected at random.NARREND -{Marital Status Narrative} Develop the joint probability table.

Thomas ____________________ first employed the calculation of conditional probability.

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

NARRBEGIN: Hobby Shop Sales Hobby Shop Sales Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks. Number of Trucks Sold Number of Weeks 0 20 1 15 2 10 3 4 4 1 NARREND -{Hobby Shop Sales Narrative} Define the random experiment of interest to the store.

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.P(B)

NARRBEGIN: Cysts Cysts After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign. A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not). The doctor has discovered the same type of cyst in a patient.NARREND -{Cysts Narrative} What is the probability that the patient will test negative?

A posterior probability value is a prior probability value that has been:

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

NARRBEGIN: CertificationTest 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.NARREND -{Certification Test Narrative} If the selected candidate passed the test, what is the probability that the candidate took the test at location B?

NARRBEGIN: Marital Status Marital Status An insurance company has collected the following data on the gender and marital status of 300 customers. Marite Status Gander Single Maried Divorced Male 25 125 30 Female 50 50 20 Suppose that a customer is selected at random.NARREND -{Marital Status Narrative} Is marital status independent of gender? Explain using probabilities.

Two events A and B are said to be independent if P(A|B) = P(B).

NARRBEGIN: Cysts Cysts After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign. A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not). The doctor has discovered the same type of cyst in a patient.NARREND -{Cysts Narrative} In the absence of any test, what is the probability that the cyst is malignant?

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} Express each of the following probabilities in words: a.P(A|B) b.P(B|A)

In general, a posterior probability is calculated by adding the prior and likelihood probabilities.

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} Which approach was used to produce this figure?

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 is the most common interest rate?

If two events are independent, what is the probability that they both occur?

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

NARRBEGIN: Construction Bids 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.NARREND -{Construction Bids Narrative} What is the probability that the company will win neither contract?

There are three approaches to determining the probability that an outcome will occur: classical, relative frequency, and subjective. For each situation that follows, determine which approach is most appropriate. a.A Russian will win the French Open Tennis Tournament next year. b.The probability of getting any single number on a balanced die is 1/6. c.Based on the past, it's reasonable to assume the average book sales for a certain textbook is 6,500 copies per month.