Experimental Probability Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Experimental Probability.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

The probability of an event based on actual experimental data: the number of times the event occurred divided by total trials.

You flip a coin 100 times and get 53 heads. Your experimental probability is \frac{53}{100} = 0.53. It's based on what DID happen, not what should happen theoretically.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Experimental probability is observed frequency from actual trials. It approaches theoretical probability as the number of trials increases.

Common stuck point: Students expect experimental results to exactly match theoretical probability. Short-run results vary widely; only many trials produce reliable estimates.

Worked Examples

Example 1

easy
A student flips a coin 50 times and gets 28 heads and 22 tails. What is the experimental probability of getting heads?

Solution

  1. 1
    Step 1: Experimental probability = \frac{\text{number of times event occurred}}{\text{total number of trials}}.
  2. 2
    Step 2: P(\text{heads}) = \frac{28}{50} = 0.56 or 56%.
  3. 3
    Step 3: This is close to but not exactly 0.5 (the theoretical probability), which is expected because experimental probability varies from trial to trial.

Answer

The experimental probability of heads is \frac{28}{50} = 0.56 (56%).
Experimental probability is based on actual observations from an experiment, not on theoretical calculations. It may differ from the theoretical probability, especially with a small number of trials. As the number of trials increases, experimental probability tends to approach the theoretical value.

Example 2

medium
A bag contains an unknown number of red and blue marbles. In 80 draws (with replacement), 52 red and 28 blue marbles were drawn. (a) Estimate the probability of drawing a red marble. (b) If there are 20 marbles total, estimate how many are red.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A spinner has sections coloured red, blue, and green. After 120 spins, the results are: Red 45, Blue 50, Green 25. (a) Find the experimental probability of each colour. (b) Do you think the spinner is fair (equal sections)? Justify your answer.

Example 2

hard
A basketball player made 72 out of 100 free throws in practice. (a) What is her experimental free-throw probability? (b) In the next game, she attempts 15 free throws. How many would you expect her to make? (c) Why might the actual number differ from your prediction?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

probability basicdata collection