HOW TO USE THE LAB
Step 1: Congratulations! You have been hired to help Rick and Athena manage the U.S. tour of The Probabilities, one of the hottest new bands around. Your goal is to make enough money from ticket sales to pay for the expenses of the tour with enough left over for the band to produce a new CD. Start by selecting the number of cities you wish to visit on your tour, then click "Get Started." You will play three concerts in each city.
Step 2: Next choose a city from the U.S. map and click the orange question mark icon. Review how much it will cost to hold each concert, how much you can earn from each concert, and the probability of having a successful concert.
As you know, the music business can be tough and sometimes things don't work out as expected. For example, if it rains before a concert on an outdoor stage, your fans might not show up. If a concert fails, you will still have to pay the expenses.
Step 3: Based on the data, choose whether or not you want to book concerts in this city. Consider the city's expenses, revenues, and probability of success. However, remember that the probability of success shown on the screen is the theoretical probability. Your actual experience might be different. For example, if the theoretical probability of success were 2/3, you would expect two concerts to be successful and one to fail. However, your actual experience might be that zero, one, two, or three concerts are successful.
Step 4: When you choose a city, click "Book It!", and you will be taken to the probability wheel for the city you picked. For a city with a 7/10 chance of success, seven segments of the wheel will have the success icon and three segments will indicate failure.
Step 5: Click "Spin" to discover whether your concert was a success or a failure. After each spin, you'll see how much you made or lost on the concert. Repeat until all three concerts are completed. If this stop on the tour was a success, you'll have earned money at the end of the three concerts. If not, you'll have lost money after the three concerts.
Step 6: After you have completed your concerts in a city, you will have the chance to earn extra money by correctly answering a question involving probability. Then it's back to the map to select the next city on your band tour. The process will repeat until you have visited the number of cities you selected at the beginning of the game.
Good luck and rock on!
Step 2: Next choose a city from the U.S. map and click the orange question mark icon. Review how much it will cost to hold each concert, how much you can earn from each concert, and the probability of having a successful concert.
As you know, the music business can be tough and sometimes things don't work out as expected. For example, if it rains before a concert on an outdoor stage, your fans might not show up. If a concert fails, you will still have to pay the expenses.
Step 3: Based on the data, choose whether or not you want to book concerts in this city. Consider the city's expenses, revenues, and probability of success. However, remember that the probability of success shown on the screen is the theoretical probability. Your actual experience might be different. For example, if the theoretical probability of success were 2/3, you would expect two concerts to be successful and one to fail. However, your actual experience might be that zero, one, two, or three concerts are successful.
Step 4: When you choose a city, click "Book It!", and you will be taken to the probability wheel for the city you picked. For a city with a 7/10 chance of success, seven segments of the wheel will have the success icon and three segments will indicate failure.
Step 5: Click "Spin" to discover whether your concert was a success or a failure. After each spin, you'll see how much you made or lost on the concert. Repeat until all three concerts are completed. If this stop on the tour was a success, you'll have earned money at the end of the three concerts. If not, you'll have lost money after the three concerts.
Step 6: After you have completed your concerts in a city, you will have the chance to earn extra money by correctly answering a question involving probability. Then it's back to the map to select the next city on your band tour. The process will repeat until you have visited the number of cities you selected at the beginning of the game.
Good luck and rock on!
ABOUT PROBABILITY
You may not know it, but every time you played a board game or checked a weather report, you were considering probability! In the Probabilities Tour, you will be spinning a wheel to determine whether or not you earned money on a concert. The rule is that if you land on green segment of the wheel, you win. The number of green spaces divided by the total number of spaces (green and red) is the probability of success.
In the wheel shown above, the theoretical probability of landing on a green space is 7 (the number of green spaces) out of 10 (the total number of spaces on the wheel). That means your theoretical probability of winning is 7 out of 10. “Yes! Pretty good chance of winning,” you think. But you could land on a red space, meaning you would lose.
If you performed a test with the spinner and you spun the wheel ten times, you might land on a green space one, two, three, four, five, six, seven, eight, nine, or ten times or you might not land on a green space at all. In your ten-spin test, the number of times you land on money is your experimental probability. You won’t make money every time you spin, so to be successful on the Probabilities Tour, you will have to make good decisions based on the data you have about each city and your knowledge of probability.
In the wheel shown above, the theoretical probability of landing on a green space is 7 (the number of green spaces) out of 10 (the total number of spaces on the wheel). That means your theoretical probability of winning is 7 out of 10. “Yes! Pretty good chance of winning,” you think. But you could land on a red space, meaning you would lose.
If you performed a test with the spinner and you spun the wheel ten times, you might land on a green space one, two, three, four, five, six, seven, eight, nine, or ten times or you might not land on a green space at all. In your ten-spin test, the number of times you land on money is your experimental probability. You won’t make money every time you spin, so to be successful on the Probabilities Tour, you will have to make good decisions based on the data you have about each city and your knowledge of probability.
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.
$0
Cities Selected: 1 of 15
Salt Lake City, UT+1000
Salt Lake City, UT+1000
$400
Celebrity Gossip magazine estimates that the probability of The Probabilities having a top-ten hit is 5/8. The equivalent percentage is:
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
Step 1: Congratulations! You have been hired to help Rick and Athena manage the U.S. tour of The Probabilities, one of the hottest new bands around. Your goal is to make enough money from ticket sales to pay for the expenses of the tour with enough left over for the band to produce a new CD. Start by selecting the number of cities you wish to visit on your tour, then click "Get Started." You will play three concerts in each city.
Step 2: Next choose a city from the U.S. map and click the orange question mark icon. Review how much it will cost to hold each concert, how much you can earn from each concert, and the probability of having a successful concert.
As you know, the music business can be tough and sometimes things don't work out as expected. For example, if it rains before a concert on an outdoor stage, your fans might not show up. If a concert fails, you will still have to pay the expenses.
Step 3: Based on the data, choose whether or not you want to book concerts in this city. Consider the city's expenses, revenues, and probability of success. However, remember that the probability of success shown on the screen is the theoretical probability. Your actual experience might be different. For example, if the theoretical probability of success were 2/3, you would expect two concerts to be successful and one to fail. However, your actual experience might be that zero, one, two, or three concerts are successful.
Step 4: When you choose a city, click "Book It!", and you will be taken to the probability wheel for the city you picked. For a city with a 7/10 chance of success, seven segments of the wheel will have the success icon and three segments will indicate failure.
Step 5: Click "Spin" to discover whether your concert was a success or a failure. After each spin, you'll see how much you made or lost on the concert. Repeat until all three concerts are completed. If this stop on the tour was a success, you'll have earned money at the end of the three concerts. If not, you'll have lost money after the three concerts.
Step 6: After you have completed your concerts in a city, you will have the chance to earn extra money by correctly answering a question involving probability. Then it's back to the map to select the next city on your band tour. The process will repeat until you have visited the number of cities you selected at the beginning of the game.
Good luck and rock on!
Step 2: Next choose a city from the U.S. map and click the orange question mark icon. Review how much it will cost to hold each concert, how much you can earn from each concert, and the probability of having a successful concert.
As you know, the music business can be tough and sometimes things don't work out as expected. For example, if it rains before a concert on an outdoor stage, your fans might not show up. If a concert fails, you will still have to pay the expenses.
Step 3: Based on the data, choose whether or not you want to book concerts in this city. Consider the city's expenses, revenues, and probability of success. However, remember that the probability of success shown on the screen is the theoretical probability. Your actual experience might be different. For example, if the theoretical probability of success were 2/3, you would expect two concerts to be successful and one to fail. However, your actual experience might be that zero, one, two, or three concerts are successful.
Step 4: When you choose a city, click "Book It!", and you will be taken to the probability wheel for the city you picked. For a city with a 7/10 chance of success, seven segments of the wheel will have the success icon and three segments will indicate failure.
Step 5: Click "Spin" to discover whether your concert was a success or a failure. After each spin, you'll see how much you made or lost on the concert. Repeat until all three concerts are completed. If this stop on the tour was a success, you'll have earned money at the end of the three concerts. If not, you'll have lost money after the three concerts.
Step 6: After you have completed your concerts in a city, you will have the chance to earn extra money by correctly answering a question involving probability. Then it's back to the map to select the next city on your band tour. The process will repeat until you have visited the number of cities you selected at the beginning of the game.
Good luck and rock on!