Probability (Intro) • Topic 2 of 2

Experimental vs Theoretical Probability

There are two types of probability:

Type	Definition	Example
Theoretical Probability	What SHOULD happen mathematically	P(heads) = 1/2
Experimental Probability	What ACTUALLY happens in trials	48 heads in 100 flips => P = 0.48

Law of Large Numbers: As the number of trials increases, experimental probability gets closer and closer to theoretical probability.

Experimental P = (number of times event occurred) / (total number of trials)

EXPERIMENTAL vs THEORETICAL (Coin Flip):

Trials:   10    30    50    80    100
Exp P:   0.70  0.60  0.55  0.52  0.50
Theo P:  --------0.50 (constant)--------

As trials increase, experimental approaches theoretical!

KEY DIFFERENCE:
  Theoretical: based on math/logic (before experiment)
  Experimental: based on actual results (after experiment)

Solved Examples

Worked Example

A die is rolled 60 times. Number 3 appears 12 times. Find experimental P(3). Compare to theoretical.

SolutionExperimental P(3) = 12/60 = 0.2. Theoretical P(3) = 1/6 ≈ 0.167. Very close!

Worked Example

A spinner with 4 equal sections (A,B,C,D) is spun 50 times. A came up 12 times. Find experimental P(A).

SolutionExperimental P(A) = 12/50 = 0.24. Theoretical P(A) = 1/4 = 0.25. Nearly equal.

Key Points

Experimental probability = observed frequency / total trials
Theoretical probability = expected mathematically (perfect world)
More trials = experimental closer to theoretical (Law of Large Numbers)
Use experimental probability when theoretical is unknown

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.Theoretical probability $=$

Explanation: Favourable over total outcomes.

Q2.Experimental probability $=$

Explanation: Based on actual trials.

Q3.As the number of trials increases, experimental probability approaches the ___ probability.

Explanation: Theoretical.

Q4.A coin tossed $100$ times shows $60$ heads. The experimental $P(\text{head})$ is:

Explanation: $60/100$.

Practice more MCQs → 📝 Assignment · 35 marks