Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 8, Part C:
Analyzing Binomial Probabilities (45 minutes)

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

 A tree diagram is a helpful tool for determining theoretical or mathematical probabilities. Let's begin by examining the problem of tossing a fair coin. We'll focus on the number of heads that occur in a certain number of tosses. Note 7 A tree diagram for the toss of a single coin has two branches that represent the two possible outcomes of this random experiment. In this tree diagram, the red branch represents the outcome "heads" (H), and the blue branch represents the outcome "tails" (T): For a single toss, the outcome is either heads or tails. Since we're looking at the number of heads that occur, the possible values from one toss are either 1 (heads) or 0 (tails). We can extend the tree diagram to show more than one coin toss. Use the Interactive Activity to see how we construct the diagram. Try several rounds of two, three, and four tosses, and record your outcomes.

This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. For those who prefer, there is a non-interactive version of this activity.

 Video Segment In this video segment, Professor Kader demonstrates how to construct a tree diagram. As you watch, ask yourself, What does a path on a tree diagram represent? View this segment after you've completed the Interactive Activity. Note: In the experiment conducted by the onscreen participants, participants tried to guess whether dice would land on an even or an odd number. If their guess was correct, the outcome was labeled "C"; if incorrect, the outcome was labeled "I." If you're using a VCR, you can find this segment on the session video approximately 14 minutes and 35 seconds after the Annenberg Media logo.

 Session 8: Index | Notes | Solutions | Video