 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 8, Part C:
Analyzing Binomial Probabilities

In This Part: Making a Tree Diagram | Probability Tables | Binomial Experiments
Pascal's Triangle

Our coin tosses have been an example of a binomial experiment. A binomial experiment consists of n trials, where each trial is like a coin toss with exactly two possible outcomes. In each trial, the probability for each outcome remains constant.

In the previous section, we used a tree diagram to help us determine one particular outcome of a binomial experiment of n = 4 trials: the number of heads resulting from four tosses of a fair coin. These outcomes can be represented by the table you created in Problem C4:   Frequency Probability  0 1 1/16 1 4 4/16 2 6 6/16 3 4 4/16 4 1 1/16 Let's take a look at the patterns that emerge when you run this binomial experiment several times, each time increasing the number of trials:

One Toss   Frequency  0 1 1 1 Two Tosses   Frequency  0 1 1 2 2 1 Three Tosses   Frequency  0 1 1 3 2 3 3 1 Four Tosses   Frequency  0 1 1 4 2 6 3 4 4 1 If you display these possible outcomes in the following format, you'll find that they form what's known as Pascal's Triangle:    Session 8: Index | Notes | Solutions | Video