Experimental vs Theoretical Probability

Grade 4

Two ways to find probability

Theoretical probability is what you calculate. You assume all outcomes are equally likely and use the formula. A fair coin: P(heads) = ½. You never need to actually flip it.

Experimental probability (also called relative frequency) is what you measure. You run an experiment — flip the coin, spin the spinner, roll the dice — count the results, and estimate from real data.

Experimental probability = number of times event occurred ÷ total number of trials

Worked example

EXAMPLE
A spinner is spun 200 times. It lands on blue 70 times. (a) What is the experimental probability of blue? (b) If the spinner were fair with 4 equal sections, what would the theoretical probability of blue be?
(a) Experimental probability = 70 ÷ 200 = 0.35. (b) Theoretical probability = 1 ÷ 4 = 0.25. The experimental value is higher than expected — this suggests the spinner might be biased towards blue.

More trials = better estimate

The more trials you run, the closer experimental probability gets to the true theoretical value. With only 10 flips of a fair coin you might get 7 heads — that looks odd. With 10 000 flips you'll be very close to 5000 heads.

Exam questions sometimes ask: "How could you make the estimate more reliable?" The answer is always increase the number of trials.

When to use each

Use theoretical probability when a situation is fair and you can list all outcomes. Use experimental probability when you're dealing with something biased, real-world, or unknown — like the probability a drawing pin lands point-up. You can't calculate that; you have to measure it.
Nova
Try this one

A bag contains 5 red counters, 3 blue counters and 2 green counters.

A counter is chosen at random.

(a) Write down the probability that the counter is red. [1]

(b) Write down the probability that the counter is not green. [1]

(c) Write down the probability that the counter is yellow. [1]

Nova's hint:

This uses the concept of basic probability — finding the likelihood of an event by counting favourable outcomes.

Ask yourself: 'How many counters satisfy this condition, and how many counters are there in total?' Try writing a fraction with the total in the denominator first, then fill in the numerator by counting.

Try to Solve it with Nova?