Theoretical vs Experimental Probability

Theoretical vs. Experimental Probability

1. Identify the type of probability

   • Theoretical probability is based on the number of favorable outcomes and the total number of equally likely outcomes.
   • Experimental probability is based on results from trials or data collected.

2. Write the fraction correctly

   • Theoretical:

     [ P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total possible outcomes}} ]

   • Experimental:

     [ P(\text{event}) = \frac{\text{number of times the event occurs}}{\text{total number of trials}} ]

3. Simplify the answer

   • Reduce the fraction to lowest terms when possible.
   • If the problem asks for a decimal or percent, convert after simplifying.

4. Compare if needed

   • Theoretical probability tells what should happen in an ideal situation.
   • Experimental probability tells what actually happened in the given trials.
   • These values may be close, but they do not have to be the same.

5. Check your work

   • Make sure the numerator matches the event asked about.
   • Make sure the denominator matches the correct total: outcomes for theoretical, trials for experimental.
   • Your final answer should be reasonable and between 0 and 1.

This method helps you solve each problem accurately and keep your final answer simplified.