How to Use Event Grids to Teach Probability

For students of introductory probability, the calculation and interpretation of probabilities of individual events is a basic task. However, when students are introduced to the concepts of intersections and unions of events, the calculation of probabilities becomes a complex affair. Event grids are graphs that can help students visualize the interactions of two events. From these grids, students can easily grasp the meaning of intersections and unions of events and compute probabilities in a more efficient way.

Instructions

    • 1

      Introduce and explain event grids. Students should know that event grids are tables with events for the rows and columns. Introduce event grids through examples. One example is an event grid where columns represent number appearing at the roll of a dice; the columns should contain the numbers 1 through six. The rows can be the flip of a coin; thus there are two rows: "heads" and "tails."

    • 2

      Add probabilities to the event grids. The probabilities for each event should appear at the margin below (for columns) or to the right (for rows). Ffor the example, there should be "1/6" at the bottom of each column and "1/2" at the right of each row.

    • 3

      Teach intersections. The intersections of the events are simply the cells corresponding to the events. For example, to calculate the probability of P(A and B), where A = {even} and B = {heads}, you would only evaluate the cells that match on these criterion. In this case, the cells in row "heads" matching "2," "4" and "6." Are the cells used in the calculation. Write the probability of these intersections in the cells. Show that these probabilities are the margins multiplied by each other. The cell corresponding to "1" and "T" is (1/6)(1/2) or 1/12.

    • 4

      Teach unions. Show that the unions correspond to the sum of the margins minus the intersections corresponding to the events. For example, the union P(A or B), where A = {even} and B = {heads} is 1/2 + 1/2 -- (3*1/12), or 3/4.

    • 5

      Demonstrate the second axiom of probability. You can do this after immediately after teaching intersections, if desired. The second axiom of probability states that P(Z) = 1, where Z is the entire set of events. Students can add up all the cells in the event grid to find that the probability sums to one. For our example, we have 12*(1/12), which is exactly 1.

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