Session 8, Part C:
Analyzing Binomial Probabilities

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. Complete the exercise below to see how we construct the diagram. Try several rounds of two, three, and four tosses, and record your outcomes.

 Let's expand our tree diagram to two tosses of a fair coin. Again, each red branch represents the result heads, and each blue branch represents the result tails. The tree diagrams below illustrate the four possible paths along the branches when you toss a coin twice: Path 1: First Toss -- Heads, Second Toss -- Heads (Abbreviated HH): Path 2: First Toss -- Heads, Second Toss -- Tails (Abbreviated HT): Path 3: First Toss -- Tails, Second Toss -- Heads (Abbreviated TH): Path 4: First Toss -- Tails, Second Toss -- Tails (Abbreviated TT):

 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