Exam 6: Probability

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 Sald Number af Weeks 0 20 1 15 2 10 3 4 4 1 -{Hobby Shop Sales Narrative} List the outcomes in the sample space.

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 student selected is in the upper class,what is the probability that her GPA is between 2.0 and 3.0?

{Marital Status Narrative} Is marital status independent of gender? Explain using probabilities.

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?

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 P(A)= .30,P(B)= .60,and P(A and B)= .20,then P(A|B)= .40.

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 lower class and has GPA over 3.0?

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 neither condo sales nor interest rates will increase during the next six months?

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} If a bank is selected at random from this distribution,what is the probability that the interest rate charged on a home loan exceeds 7.0%?

If P(A|B)= P(A)then events A and B are ____________________.

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 most one of the two contracts?

Which of the following statements is always correct?

A survey of a magazine's subscribers indicates that 50% own a house,80% own a car,and 90% of the homeowners also own a car.What proportion of subscribers: a. own both a car and a house? b. own a car or a house,or both? c. own neither a car nor a house?

Tea and Seltzer Suppose 55 percent of adults drink tea,45 percent drink seltzer,and 10 percent drink both. -{Tea and Seltzer Narrative} What is the probability that a randomly chosen adult drinks seltzer or tea or both?

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

Which of the following best describes the concept of marginal probability?

If an experiment consists of five outcomes with P(O₁)= 0.10,P(O₂)= 0.20,P(O₃)= 0.30,P(O₄)= 0.25,then P(O₅)is

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 benign tumor if he or she tests positive?

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 the probability that a package was delivered on time.

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