Seventh Grade · Math · week 33

Experimental versus theoretical probability

Compare experimental probability, based on collected data, to theoretical probability, calculated from equally likely outcomes.

Theoretical probability is calculated ahead of time from equally likely outcomes, like P(heads) = 1/2 for a fair coin. Experimental probability instead comes from actually trying something and counting: (number of times the event happened) / (total number of trials).

The two usually do not match exactly, especially with few trials -- that difference is normal random variation, not a mistake. As the number of trials grows very large, experimental probability tends to drift closer and closer to the theoretical probability.

📋 For the teacher
Teach it (10–15 min):
  • Actually run a small trial together -- flip a coin 20 times, or roll a die 30 times, and compute the real experimental probability.
  • Compare the experimental result to the theoretical prediction out loud, and talk about why they are close but likely not identical.
  • Introduce the idea that MORE trials generally means experimental probability gets closer to theoretical -- more data smooths out the lucky or unlucky streaks.
  • Avoid saying a fair result is "wrong" if it does not match theory perfectly on a small sample -- that variation is expected.
Talk about it:
  • What is the difference between experimental and theoretical probability?
  • Why might 10 coin flips give very different results than 1,000 coin flips?
  • Can experimental probability ever be more useful than theoretical probability? When?

Mastery looks like: They correctly compute an experimental probability from trial data and explain how it relates to the theoretical probability.

Common stumbles: Assuming experimental and theoretical probability must match exactly; treating a small-sample mismatch as a sign of a broken or unfair device.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
← Back to todayAll coursesYear planner