How to Teach Probability With Interactive Coins


Many people have found themselves in this position: A friend flips a coin, you shout "heads" and one of you winds up paying the restaurant tab. From an initial coin toss a person has a 50 percent chance of winning. However, if there are multiple coin tosses, such as "best two out of three," the probability that a person will win with "heads" can change. Interactive coin tosses provide great teaching tools to help students understand the laws of probability.

Empirical Probability

  • An event or action that deploys empirical probability uses data to "estimate" event outcomes based on how often the event takes place. Determining empirical probability requires experiments, trials and direct observations in order to get the needed data. A teacher can introduce her students to empirical probability by giving each student a penny, a piece of paper and a pencil. Have students number their paper 1-10 and have them flip the penny 10 times, recording the outcomes. Instruct students to state which outcome was greater. Once the data has been recorded, have your students repeat the exercise. According to empirical probability your class can predict the next outcome based on previous individual student and group results.

Theoretical Probability

  • Theoretical probability can be determined by using the ratio of the number of favorable outcomes over the total number of possible outcomes. A coin is a perfect device for teaching theoretical probability. Get your class of students engaged before you demonstrate a coin toss. Ask them if they have ever seen a coin toss before an NFL football game and ask a student to "call it" as if he was Aaron Rodgers. Once you get that answer from the class, implement it into your formula. Take a silver dollar and ask what the probability is that a tail will face upwards. Tell the class that their choice is the favorable one. For example, if they say "tails," that would be the favorable outcome, and there is a 50 percent chance it will land accordingly. The option of tossing "tails" is 1 out of 2.


  • Nonprobability is a method for gathering data, but it does not rely on in-depth analysis. Ask students to empty their pockets, as some are bound to have coins there. Have the class make an equation using the total number of students and those with coins in their pockets. This will illustrate a random method lacking any analysis, adhering to a nonprobability model. Nonprobability saves researchers time, money and effort but at the expense of detailed information and credibility. Nonprobability normally is used when researchers want to formulate an idea about a phenomena that can involve people, places or objects. Canada's Department of Statistics says that since elements are chosen arbitrarily, there isn't a way to estimate the probability of any one element in a nonprobability sample.

Probability and Counting

  • Take 10 coins and paint them in pairs so each pair has a separate color: two red, two blue, etc. Place five differently colored coins in a bag and have students count the possible outcome for drawing a single color (1 in 5). Then place all 10 coins in the bag and ask them the probability of blindly drawing a matching set of colored coins. Break the concept down in gradual stages, as comprehending the probability of drawing two red coins at once takes greater math skills than simply dividing one into five. Counting is relevant to finding probability outcomes and is the basic skill required for completing formulas. If a student plans to work in big banking or work as a scout for a sports team he will need to know how to use counting within the realms of probability predictions.

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