HOW TO USE THE LAB
1. Coins, dice, and spinner wheels are all tools that demonstrate probability. Imagine that you would like to conduct a probability experiment using one of these tools. Flipping a coin 500 times, recording the results, and calculating the experimental probability would take quite a while. Rather than using actual coins, dice, or spinners, the Probability Lab runs experiments in a matter of seconds. To run your own experiment, choose a coin, a die, or a spinner and select an outcome to test using one of these tools.
EXAMPLE 1:
The number of times you can roll an even number on a die.
EXAMPLE 2:
The number of times you can spin a 10 on a spinner with twelve different numbers on it.
2. Calculate the theoretical probability by identifying how many times your selected outcome could occur out of the total number of possible outcomes.
EXAMPLE 1:
There are even numbers on three sides of the die and there are six sides in all, so the theoretical probability of rolling an even number would be 1 out of 2 (reduced to the lowest terms from3 out of 6).
EXAMPLE 2:
There is one 10 on the spinner and twelve total numbers on the spinner, so the probability of spinning a 10 would be1 out of 12.
3. Enter your probability in the “Select Theoretical Probability” box and click the “Get Started” button.
4. On the next screen, enter the number of times you’d like the Probability Lab to virtually flip the coin, roll the die, or turn the spinner and click “Go.” The results bar in the middle of the screen will tell you how many times your outcome occurred. How close did the results of your experiment match the theoretical probability?
5. Now repeat the experiment with more tries. Pay attention to how your experimental probability changes in relation to the theoretical probability as you add more tries to the experiment. Run the experiment three more times, increasing the number of tries each time.
6. After five experiments, review your results and reflect on what you learned about theoretical probability and experimental probability. Did a larger number of tries take your results closer to the theoretical probability? Discuss your findings with a classmate or your teacher, or write down your responses in your math notebook.
EXAMPLE 1:
The number of times you can roll an even number on a die.
EXAMPLE 2:
The number of times you can spin a 10 on a spinner with twelve different numbers on it.
2. Calculate the theoretical probability by identifying how many times your selected outcome could occur out of the total number of possible outcomes.
EXAMPLE 1:
There are even numbers on three sides of the die and there are six sides in all, so the theoretical probability of rolling an even number would be 1 out of 2 (reduced to the lowest terms from3 out of 6).
EXAMPLE 2:
There is one 10 on the spinner and twelve total numbers on the spinner, so the probability of spinning a 10 would be1 out of 12.
3. Enter your probability in the “Select Theoretical Probability” box and click the “Get Started” button.
4. On the next screen, enter the number of times you’d like the Probability Lab to virtually flip the coin, roll the die, or turn the spinner and click “Go.” The results bar in the middle of the screen will tell you how many times your outcome occurred. How close did the results of your experiment match the theoretical probability?
5. Now repeat the experiment with more tries. Pay attention to how your experimental probability changes in relation to the theoretical probability as you add more tries to the experiment. Run the experiment three more times, increasing the number of tries each time.
6. After five experiments, review your results and reflect on what you learned about theoretical probability and experimental probability. Did a larger number of tries take your results closer to the theoretical probability? Discuss your findings with a classmate or your teacher, or write down your responses in your math notebook.
ABOUT PROBABILITY
You may not know it, but every time you played a board game or checked a weather report, you have considered probability! Imagine you are playing a game with a six-sided die. The situation is if you roll anything but a 4, you win.
The theoretical probability of landing on a 4 is one (the number of sides with a 4) out of six (the total number of sides the die could land on). That means your theoretical probability of winning is five out of six. “Yes! Pretty good chance of winning,” you think, but you know that you could roll a 4.
If you performed a test with a six-sided die and rolled it six times, a 4 might come up one, two, three, four, five, or six times or it might not come up at all. In your six-roll test, if 4 came up twice, then the experimental probability of rolling a 4 is 1/3 (2/6 reduced to lowest terms.)
In real life, making decisions would be a lot easier if we know exactly what the future would bring. Since we can’t know the future with certainty, theoretical probability gives us a reasonable idea of what to expect. However, as you will find in this lab, real life doesn’t always turn out as expected.
The theoretical probability of landing on a 4 is one (the number of sides with a 4) out of six (the total number of sides the die could land on). That means your theoretical probability of winning is five out of six. “Yes! Pretty good chance of winning,” you think, but you know that you could roll a 4.
If you performed a test with a six-sided die and rolled it six times, a 4 might come up one, two, three, four, five, or six times or it might not come up at all. In your six-roll test, if 4 came up twice, then the experimental probability of rolling a 4 is 1/3 (2/6 reduced to lowest terms.)
In real life, making decisions would be a lot easier if we know exactly what the future would bring. Since we can’t know the future with certainty, theoretical probability gives us a reasonable idea of what to expect. However, as you will find in this lab, real life doesn’t always turn out as expected.
PROBABILITY IN EVERYDAY LIFE
The Probability Lab uses the idea of coin flips, die tosses, and
game wheel spins to explore the basics of probability. In real
life, however, probability is much more complex. The
probability of a team winning a game or a class doing well on a
test has many more possible outcomes than the two sides of a
coin or the six sides of a die. Here are some of the ways that
probability is used in everyday life:
- Weather Prediction
A meteorologist uses current and historical observations/data, computer modeling techniques, and scientific and mathematical knowledge to develop a forecast. If the meteorologist on television says there is a 90% chance of rain, it is more likely that you will carry an umbrella than if there is a 10% chance. - Polling
News organizations use probability when they take a sample of some of the voters leaving polling places and declare that a candidate for election will be the winner even before all the votes are counted. - Advising Businesses
An actuary uses probability when advising an insurance company on the price to charge for an insurance policy.
THEORETICAL PROBABILITY:
1 OUT OF 1: 100% : 1
90%
EXPERIMENT RESULTS
Review the results of your experiment.
The experimental probability is the number of times your event occured divided by the total number of tries. Out of your total number of tries, how many times did your event occur? Was the experimental probability higher, lower than, or the same as the theoretical probability?
Now repeat the experiment four more times with larger numbers in the “INPUT THE NUMBER OF TRIES” box. As you add more tries to the experiment, notice how the experimental probability changes in relation to the theoretical probability.
The experimental probability is the number of times your event occured divided by the total number of tries. Out of your total number of tries, how many times did your event occur? Was the experimental probability higher, lower than, or the same as the theoretical probability?
Now repeat the experiment four more times with larger numbers in the “INPUT THE NUMBER OF TRIES” box. As you add more tries to the experiment, notice how the experimental probability changes in relation to the theoretical probability.
RESULTS COMPLETE!
Now that you've completed your experiments, look at the results data below and consider the following questions:
- How close did the actual results (the experimental probability) come to the theoretical probability?
- Did the number of tries affect how close the experimental probability came to the theoretical probability?
- What conclusions did you draw about theoretical probability and experimental probability?
HOW TO USE THE LAB
1. Coins, dice, and spinner wheels are all tools that demonstrate probability. Imagine that you would like to conduct a probability experiment using one of these tools. Flipping a coin 500 times, recording the results, and calculating the experimental probability would take quite a while. Rather than using actual coins, dice, or spinners, the Probability Lab runs experiments in a matter of seconds. To run your own experiment, choose a coin, a die, or a spinner and select an outcome to test using one of these tools.
EXAMPLE 1:
The number of times you can roll an even number on a die.
EXAMPLE 2:
The number of times you can spin a 10 on a spinner with twelve different numbers on it.
2. Calculate the theoretical probability by identifying how many times your selected outcome could occur out of the total number of possible outcomes.
EXAMPLE 1:
There are even numbers on three sides of the die and there are six sides in all, so the theoretical probability of rolling an even number would be 1 out of 2 (reduced to the lowest terms from3 out of 6).
EXAMPLE 2:
There is one 10 on the spinner and twelve total numbers on the spinner, so the probability of spinning a 10 would be1 out of 12.
3. Enter your probability in the “Select Theoretical Probability” box and click the “Get Started” button.
4. On the next screen, enter the number of times you’d like the Probability Lab to virtually flip the coin, roll the die, or turn the spinner and click “Go.” The results bar in the middle of the screen will tell you how many times your outcome occurred. How close did the results of your experiment match the theoretical probability?
5. Now repeat the experiment with more tries. Pay attention to how your experimental probability changes in relation to the theoretical probability as you add more tries to the experiment. Run the experiment three more times, increasing the number of tries each time.
6. After five experiments, review your results and reflect on what you learned about theoretical probability and experimental probability. Did a larger number of tries take your results closer to the theoretical probability? Discuss your findings with a classmate or your teacher, or write down your responses in your math notebook.
EXAMPLE 1:
The number of times you can roll an even number on a die.
EXAMPLE 2:
The number of times you can spin a 10 on a spinner with twelve different numbers on it.
2. Calculate the theoretical probability by identifying how many times your selected outcome could occur out of the total number of possible outcomes.
EXAMPLE 1:
There are even numbers on three sides of the die and there are six sides in all, so the theoretical probability of rolling an even number would be 1 out of 2 (reduced to the lowest terms from3 out of 6).
EXAMPLE 2:
There is one 10 on the spinner and twelve total numbers on the spinner, so the probability of spinning a 10 would be1 out of 12.
3. Enter your probability in the “Select Theoretical Probability” box and click the “Get Started” button.
4. On the next screen, enter the number of times you’d like the Probability Lab to virtually flip the coin, roll the die, or turn the spinner and click “Go.” The results bar in the middle of the screen will tell you how many times your outcome occurred. How close did the results of your experiment match the theoretical probability?
5. Now repeat the experiment with more tries. Pay attention to how your experimental probability changes in relation to the theoretical probability as you add more tries to the experiment. Run the experiment three more times, increasing the number of tries each time.
6. After five experiments, review your results and reflect on what you learned about theoretical probability and experimental probability. Did a larger number of tries take your results closer to the theoretical probability? Discuss your findings with a classmate or your teacher, or write down your responses in your math notebook.