How to Graph Probabilities

Perform the event multiple times to assess the probability.

A probability graph is a visual representation of the likelihood of different outcomes occurring for a single event. The x-axis contains the possible outcomes, while the y-axis is the percent likelihood. A histogram is the most common type for graphing probabilities.

Instructions

1. Determine all of the possible outcomes of the event for which you are calculating the probabilities. For example, to graph the probabilities for a coin toss landing heads a certain number of times out of five tosses, there are six possible outcomes: P(0), P(1), P(2), P(3), P(4) and P(5).

2. Perform the event as many times as possible (the more instances of the event, the more accurate the probability graph) and observe the number of times each outcome occurs.

3. Calculate the probability of each event by dividing the number of outcomes by the number of total events. For example, if you tossed five coins 10 times, divide the number of outcomes for each number of heads by 10 to get the probability.

4. Draw the first quadrant of the xy coordinate plane (x and y both positive). Label the x-axis with each of the possible outcomes (in order if there is a logical order). Label the y-axis with probabilities from 0 to 100 percent. In the example, label the x-axis with six marks, corresponding to P(0) through 5, and the y-axis with percentages.

5. Draw a histogram plot for the data you collected in Step 2 by drawing a bar at each point on the x-axis with height corresponding to the probability you calculated for each probability. There should be no space between any of the bars and between the first bar and the y-axis.

6. Superimpose a smooth curve that approximately matches the heights of the histogram bars to show the continuous probability distribution.

References

• Mathisfun.com: Probability
• Texas A&M University Department of Mathematics: The Normal Distribution