Experimental Probability

In a Nutshell

Experimental probability (relative frequency) is found by running an experiment: P(event)=number of times the event happenedtotal number of trialsP(\text{event}) = \dfrac{\text{number of times the event happened}}{\text{total number of trials}}.

Sometimes we cannot work out a probability by counting equally likely outcomes — for example, predicting whether a drawing pin will land point-up or point-down. In these cases we do an experiment and use the results.

The relative frequency of an event is the fraction of trials in which it occurred:

Relative frequency=frequency of the eventtotal number of trials\text{Relative frequency} = \frac{\text{frequency of the event}}{\text{total number of trials}}

The more trials you carry out, the closer the relative frequency gets to the theoretical probability — this is called the law of large numbers.

Frequency experiment simulator A bar chart that grows as trials are run, showing the relative frequency of each outcome approaching the theoretical probability. Relative frequency 0.00 0.25 0.50 0.75 1.00

Trials: 0

Watch it work

Question: Priya flips a coin 50 times and gets heads 32 times. Find the experimental probability of heads.

Have a go

Q1. A die is rolled 60 times. A six appears 14 times. Find the experimental probability of rolling a six.

Q2. In 200 spins of a spinner, "blue" comes up 48 times. What is the relative frequency of blue?

Q3. Tom drops a drawing pin 100 times and it lands point-up 63 times. If he drops it again, what is his best estimate of the probability it lands point-up?

Q4. Would you trust the result more after 10 trials or 1000 trials? Explain why.