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7th Grade Math / Lesson 8: Probability Experimental vs. Theoretical

What will we be learning in this lesson?

  • In this lesson you will learn about the types of probability.
Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


  • Probability is the measure of the chance of something happening.

  • What do you think the chance is of someone in your class becoming President of the United States tomorrow?
    -If you said "no chance" you are right. Which means the probability of this happening in 0.

  • What do you think the chance is of a baby being born in the United States today?
    -This is something that is most certainly going to happen which means the probability is 1.


  • One way to express probability is as a number that has a value between 0 and 1. If the probability is 0, then there is no chance of that event happening. If the probability is 1, then that event is definitely going to happen.

  • If you think of tossing a coin, what are the chances of it landing tails side up?

    Since there are only two sides, there is a 1 in 2 chance of it landing tails up. This means that the probability is .5 (between 0 and 1)


  • A second way to express probability is as a percent.
    -Something that won't happen has a 0% probability.
    -Something that will definitely happen has a 100% probability.
    -Something that is uncertain whether it will happen or not has a probability between 0% and 100%.

  • Both the decimals and the fractions can easily be converted to fractions which means probability can also be given in fraction form.

  • The notation for probability is P(event)
    P stands for probability and the event that you want to have happen goes in the parenthesis. P(tails) would be looking for the probability of tossing a coin and it landing tails up.

Equally Likely

  • Events that have the same chance of happening are considered to be equally likely.

    -Examples of equally likely events
    1. Tossing a coin.
    2. Spinning a certain number on a spinner that is divided into even sections.
    3. Having 5 red marbles and 5 blue marbles in a bag, the chance of pulling out a red marble is equally likely to happen as pulling out a blue marble.

Experimental vs. Theoretical

  • Two types of probability are experimental and theoretical.
  • Experimental probability is when you actually perform an activity repeatedly and keep track of the results to see how often your desired outcome occurred.
    You toss a coin 50 times and keep track of how many times heads or tails landed up. The table contains your results.
    From this, we would conclude that the experimental probability of tossing a coin and it landing on heads would be

Experimental vs. Theoretical

    Theoretical probability is when you think about the event and base your probability on what should happen .

    You know that there are two sides to a coin. One heads and one tails. You would expect that since each side is equally likely to appear that flipping the coin two times would produce one head and one tail. This would lead you to conclude that the theoretical probability of tossing a coin and it landing on heads would be

  • Can you determine if events are equally likely to occur?
  • Can you distinguish between experimental and theoretical probability?
  • Go back to the classroom to get to your homework and any other items you need to attend to.