Exam 6: Probability

If two events are mutually exclusive, what is the probability that both occur at the same time?

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. -{Condo Sales and Interest Rates Narrative} What is the probability that condo sales will increase but interest rates will not during the next six months?

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.

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

The ____________________ rule says that P(A^c) = 1 - P(A).

Marital Status An insurance company has collected the following data on the gender and marital status of 570 customers. Suppose that a customer is selected at random. -{Marital Status Narrative} Find the probability that the customer selected is a. female and single b. married if the customer is male. c. not single

If A and B are independent events with P(A) = 0.35 and P(B) = 0.55, then P(A|B) is 0.35/0.55 = .64.

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

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. -{Cysts Narrative} What is the probability that the patient has a malignant cyst if he or she tests negative?

Cars Suppose X = the number of cars owned by a family in the U.S.The probability distribution of X is shown in the table below. -{Car Narrative}What is the chance that a family owns more than one car?

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 and Class Narrative} What is the probability that the student is in the upper class?

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: -{Drunk Drivers Narrative} What proportion of accidents involved more than one vehicle?

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

If A and B are ____________________ events, the joint probability of A and B is the product of the probabilities of those two events.

____________________ can find the probability that someone with a disease tests positive by using (among other things) the probability that someone who actually has the disease tests positive for it.

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. -{Condo Sales and Interest Rates Narrative} What is the probability that both condo sales and interest rates will increase during the next six months?

The intersection of two events A and B is the event that occurs when both A and B occur.

The collection of all possible events is called

A(n) ____________________ of a random experiment is a list of all possible outcomes of the experiment.