Content Area: Math

 

Index: 4.4B Grade 12 CPI 5

 

Standard: 4.4 - Data Analysis, Probability, and Discrete Mathematics

 

Strand: B - Probability

 

Cumulative Progress Indicator: 5 - The student will estimate probabilities and make predictions based on experimental and theoretical probabilities.

 

Grade: 12

 

Sample Activities:

 

·        After a unit where dependent and independent events were detailed, students are challenged by a problem containing this excerpt from The Miami Herald of May 5, 1983.  An airline jet carrying 172 people between Miami and Nassau lost its engine oil, power, and 12,000 feet of altitude over the Atlantic Ocean before a safe recovery was made. When all three engines' low oil pressure warning lights all lit up at nearly the same time, the crew's initial reaction was that something was wrong with the indicator system, not the oil pressure. They considered the possibility of a malfunction in the indication system because it's such an unusual thing to see all three with low pressure indications. The odds are so great that you won't get three indications like this. The odds are way out of sight, so the first thing you would suspect is a problem with the indication system. Aviation records show that the probability of an engine failure in any particular hour is about 0.00004. If the failures of three engines were independent, what would the probability be of them failing within one hour? Discuss why the speaker in the article would refer to such a probability as "way out of sight." Discuss situations which might make the failures of three engines not independent events.

 

·        Students keep a record of their trips through the town and whether or not they have to stop at each of the four traffic lights. After one month, the data is grouped and studied. They use their data to determine whether the timing of the lights is independent or not.

 

·        While discussing the issue of mandatory drug testing in social studies, students examine the probability of misdiagnosing people as having AIDS with a test that would identify 99% of those who are true positives and misdiagnose 3% of those who don't have AIDS. They examine situations where the prevalence of the disease is 50%, 10%, and 1% using 100,000 people as a base. They discuss the fact that, at the 1% level, 75% of the people identified as having AIDS would be false positives, the implications that fact has on mandatory testing, and potential ways to improve the predictive value of testing.