Exam 6: 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} What approach would you use in determining the probabilities for next week's sales? Assign probabilities to the outcomes.

An individual outcome of a sample space is called a(n) ____________________ event.

____________________ 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.

If events A and B cannot occur at the same time, they are called mutually exclusive.

If P(A) = 0.65, P(B) = 0.58, and P(A and B) = 0.76, then P(A or B) is:

Assume that A and B are independent events with P(A) = 0.30 and P(B) = 0.50. The probability that both events will occur simultaneously is 0.80.

Although there is a formula defining Bayes' law, you can also use a probability tree to conduct calculations.

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} What is the probability that the selected candidate took the test at location C and failed?

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

If P(A) = 0.84, P(B) = 0.76, and P(A or B) = 0.90, then P(A and B) is:

If A and B are independent, then P(A|B) = P(A) or P(B|A) = P(B).

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

If two events are mutually exclusive and collectively exhaustive, what is the probability that 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} Are being in the upper class and having a GPA over 3.0 related? Explain.

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

No matter which approach was used to assign probability (classical, relative frequency, or subjective) the one that is always used to interpret a probability is the ____________________ approach.

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

NARRBEGIN: Drunk Drivers Drunk Drivers Five 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: number of Vehieles inovelved Did alohol play a role? 1 2 3 Totals Yes 75 125 50 250 No 50 225 75 350 Totals 125 350 125 600 NARREND -{Drunk Drivers Narrative} What proportion of accidents involved alcohol and single vehicle?

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 the probability that a package was delivered on time.

NARRBEGIN: Drunk Drivers Drunk Drivers Five 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: number of Vehieles inovelved Did alohol play a role? 1 2 3 Totals Yes 75 125 50 250 No 50 225 75 350 Totals 125 350 125 600 NARREND -{Drunk Drivers Narrative} If alcohol was not involved, what proportion of the accidents were single vehicle?