Exam 6: Probability

If P(B) = .7 and P(A|B) = .7, then P(A and B) = 0.

If event A and event B cannot occur at the same time, then A and B are said to be

Suppose A and B are two independent events for which P(A) = 0.20 and P(B) = 0.60. a.Find P(A and B). b.Find P(A or B).

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 -A pharmaceutical firm has discovered a new diagnostic test for a certain disease that has infected 1% of the population. The firm has announced that 95% of those infected will show a positive test result, while 98% of those not infected will show a negative test result. a.What proportion of people don't have the disease? b.What proportion who have the disease test negative? c.What proportion of those who don't have the disease test positive? d.What proportion of test results are incorrect? e.What proportion of test results are correct?

If A and B are two independent events with P(A) = 0.9 and P(B|A) = 0.5, then P(A and B) = 0.45.

If the events A and B are independent with P(A) = 0.35 and P(B) = 0.45, then the probability that both events will occur simultaneously is:

NARRBEGIN: Tea and Seltzer Tea and Seltzer Suppose 55 percent of adults drink tea, 45 percent drink seltzer, and 10 percent drink both.NARREND -{Tea and Seltzer Narrative} What is the probability that a randomly chosen adult does not drink seltzer?

If A and B are mutually exclusive, their joint probability is ____________________.

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} If a package was delivered on time, what is the probability that it was service C?

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

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 and has GPA under 2.0?

Suppose the probability that a person owns both a cat and a dog is 0.10. Also suppose the probability that a person owns a cat but not a dog is 0.20. The marginal probability that someone owns a cat is 0.30.

NARRBEGIN: Condo Sales and Interest 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.NARREND -{Condo Sales and Interest Rates Narrative} What is the probability that neither condo sales nor interest rates will increase during the next six months?

If two events are mutually exclusive, what is the probability that one or the other occurs?

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

NARRBEGIN: Condo Sales and Interest 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.NARREND -{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?

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) = 0.50, P(B) = 0.40, and P(B|A) = 0.30. a.Find P(A and B). b.Find P(A or B). c.Find P(A|B).