The Chance Dance
Coding for the Core
Summer 2015
Initial hypothesis:
Your robot has two dance moves. It can roll forward and back in a straight line or it
can spin in place. The robot will randomly choose which move to make.
1. Run the program Dance1.ev3 on your robot. Did your robot roll straight or
spin?
2. What do you think will happen if you run the program again?
3. Can you use the results from your first program run to predict what will
happen the second time you run the program? Explain your reasoning.
4. Run the Dance1.ev3 program 4 more times. What were the results?
5. How likely do you think it is that the robot will roll forward and back in a
straight line? Explain your reasoning.
6. How likely do you think it is that the robot will spin? Explain your reasoning
The Chance Dance
Coding for the Core
Summer 2015
Data Collection and analysis:
When you run the program Dance20.ev3 the robot will make twenty dance moves in
a row. In order to record the number of each move, mark a 0 for each spin move and
a | for each straight move (forward and back is one move).
Here is an example:
Dance Example
0|00|||00|||||00||00
Number of straight moves: 11
Number of spin moves: 9
1. Now run the Dance20.ev3 program one time and record the results.
Dance 1
Number of straight moves:
Number of spin moves:
2. Based on Dance 1, what is the empirical probability of the robot making a
straight move? Explain your reasoning.
3. Based on Dance 1, what is the empirical probability of the robot making a
spin move? Explain your reasoning.
The Chance Dance
Coding for the Core
Summer 2015
4. Now we will repeat the experiment and record the results.
Dance 2
Number of straight moves:
Number of spin moves:
5. Based on Dance 2, what is the empirical probability of the robot making a
straight move?
6. Based on Dance 2, what is the empirical probability of the robot making a
spin move?
7. How do the results from Dance 1 and Dance 2 compare? Explain any
differences you see.
8. Combine Dance 1 and Dance 2 into one larger data set.
Dance 1 and Dance 2 combined
Number of straight moves:
Number of spin moves:
9. Based on both Dance 1 and Dance 2, what is the empirical probability of the
robot making a straight move?
10. Based on both Dance 1 and Dance 2, what is the empirical probability of the
robot making a spin move?
The Chance Dance
Coding for the Core
11. Repeat this process 3 more times.
Dance 3
Number of straight moves:
Number of spin moves:
Empirical probability of a straight move:
Empirical probability of a spin move:
Dance 4
Number of straight moves:
Number of spin moves:
Empirical probability of a straight move:
Empirical probability of a spin move:
Dance 5
Number of straight moves:
Number of spin moves:
Empirical probability of a straight move:
Empirical probability of a spin move:
Summer 2015
The Chance Dance
Coding for the Core
Summer 2015
12. How do the empirical probabilities for all of these dances compare?
13. What do you think is a good estimate for the "true" probability of each dance
move? Explain your reasoning.
14. Finally combine all five dances into one large data set of 100 dance moves.
All 5 Dances combined
Number of straight moves:
Number of spin moves:
Empirical probability of a straight move:
Empirical probability of a spin move:
15. Look at the results for Dance1, Dance 1 and Dance 2 combined and all 5
Dances combined.
Probability of straight move
Dance 1
Dance 1 and Dance 2
All 5 Dances
16. Do you notice a pattern?
Probability of spin move
The Chance Dance
Coding for the Core
Summer 2015
Conclusion:
1. Learn from your teacher the theoretical probability that was used to program
your robot.
Theoretical probability of straight move_________________________
Theoretical probability of spin move________________________
2. Compare this with the probabilities listed in the table above. What do you
see?
3. What happens as the sample size gets larger? Do you notice anything about
the distance between the theoretical and empirical probabilities?
4. Explain how using empirical probabilities to estimate theoretical
probabilities would be important in the real world in the real world. Please
be specific.