3.5. Theoretical and Experimental Spinners http://www.ck12.org
To go back to the question, how many times does the spinner land on blue if it is spun 500 times? The answer is
- To calculate the experimental probability of landing on blue, we have to divide by the total number of spins.
P(blue) =123
500
= 0. 246
Therefore, for this experiment, the experimental probability of landing on blue with 500 spins is 24.6%.
Do you remember how to calculate the theoretical probability from Example A? We know that the spinner has 4
equal parts (blue, purple, green, and red). In a single trial, we can assume that:
P(blue) =1
4
= 0. 25
Therefore, for our spinner example, the theoretical probability of landing on blue is 0.25. As we pointed out in
Example A, finding the theoretical probability requires no collection of data. It’s also worth mentioning that our
experimental probability was slightly farther away from the theoretical probability with 500 spins that it was with
170 spins in Example C. While, in general, increasing the number of spins will produce an experimental probability
that is closer to the theoretical probability, as we’ve just seen, this is not always the case!
Practice
- Based on what you know about probabilities, write definitions fortheoreticalandexperimentalprobability.
2..
a. What is the difference between theoretical and experimental probability?
b. As you add more data, do your experimental probabilities get closer to or further away from your
theoretical probabilities?
c. Is spinning 1 spinner 100 times the same as spinning 100 spinners 1 time? Why or why not?
A spinner was spun 750 times using Spin Spinner on the TI-84 calculator, with 1 representing blue, 2 representing
purple, 3 representing green, and 4 representing red as shown: