Probability

The formal study of probability is only a few centuries old — a youthful science! Its beginnings are covered in the first resource. The other sites provide activities that show the unexpected connection between probability and the patterns in Pascal’s triangle.

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The Beginnings of Probability http://mathforum.org/isaac/problems/prob1.html

Teachers can share some of this mathematics history as they work with students to compute probabilities for simple compound events, an NCTM expectation for students in grades 6-8. These pages present the problem that inspired the development of mathematical probability. Renaissance mathematicians Pierre de Fermat and Blaise Pascal solved the problem and fathered the study of probability. Outlined here is, first, the particular solution and then the general solution based on a central concept of probability, equally probable outcomes. MSP full record

Pascal's Triangle: Number Patterns http://mathforum.org/workshops/usi/pascal/pascal_intro.html

The site opens with how to construct the triangle, notes on its history, then several patterns to explore. Relevant to the topic of probability, the Probability/Combinatorics page explains the connection between the triangle’s entries and combinations. A question like "How many ways can I choose 2 socks if I have 5 socks in the drawer?" has its answer in Pascal’s triangle!

Pascal Triangle - History http://milan.milanovic.org/math/english/fibo/fibo0.html

More history than the student needs, this site is included here for its images of the Chinese version of the triangle, developed in the 11th century, and an early European version from the 13th century. Pascal never claimed to have invented the triangle that bears his name; seeing the triangle as written down centuries before his birth brings in evidence from original sources. (From Fibonacci Numbers and the Pascal Triangle - MSP full record)

The Smithville Families http://www.pbs.org/teachersource/mathline/lessonplans/msmp/smithville/smithville_procedure.shtm

In this lesson, students will use Pascal's triangle and its relationship to theoretical probability to solve a problem. The challenge is to determine the total number of possible girl/boy combinations in a five-child family and the probability of each combination. They will discover that the famous triangle relates directly to this problem scenario! The lesson plan is complete, including objectives, questions for discussion, extensions and connections. MSP full record

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Copyright January 2008 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.