Given a set of urns, each filled with a mix of black chips and white chips, what is the probability of drawing a black chip from the last urn after some sequential random shifts of chips among the urns? The Total Probability Formula (TPF) is the common tool to solve such a problem. However, when the number of urns is more than two and the number…

It is very well known that the Cauchy-Schwarz inequality is an important property shared by all inner product spaces and the inner product induces a norm on the space. A proof of the Cauchy-Schwarz inequality for real inner product spaces exists, which does not employ the homogeneous property of the inner product. However, it is shown that a real…

Presents an application of the binomial distribution in which the distribution is used to detect differences between the sensory properties of food products. Included is a BASIC computer program listing used to generate triangle and duo-trio test results. (JN)

This short note introduces an interesting random walk on a circular path with cards of numbers. By using high school probability theory, it is proved that under some assumptions on the number of cards, the probability that a walker will return to a fixed position will tend to one as the length of the circular path tends to infinity.

This report describes how an innovative curriculum promoted the civic development of high school students along with parents by stimulating news media attention and discussion in families. Evidence is based on a three-year evaluation of Kids Voting USA, an interactive, election-based curriculum. Political communication in the home increased the…

This report provides estimates of job and occupational mobility by demographic, educational and labour market variables using data from the Australian Bureau of Statistics (ABS) "Labour Mobility" survey for 2002. The report provides information on the effects of these variables on the probability of job separation. It also identifies the…

There is a strong and consistent relationship between PSAT/NMSQT scores and AP Examination grades for nearly all courses--higher scores on the PSAT/NMSQT indicate a higher probability of success on AP Examinations. PSAT/NMSQT verbal or mathematics scores are often more highly related to AP Examination grades than overall high school GPA, number of…

This publication contains Arizona public schools' academic standards for grade 2. The contents of this document include the following: (1) The Arts Standard 2006--Grade 2; (2) Comprehensive Health Education/Physical Activity Standards 1997--Foundations (Grades 1-3); (3) Foreign and Native Language Standards 1997--Foundations (Grades 1-3); (4)…