Probability from experiments
Experimental probability is the probability of an event found by actually carrying out an experiment or trial many times and recording the results. It is also called the relative frequency of the event.
Key idea
Experimental probability of an event = (number of times the event occurs) ÷ (total number of trials).
Carrying out trials
Each time we perform the experiment once, that is called a trial. For example, tossing a coin once is one trial. When we repeat the trial many times and count how often an event happens, we can write the experimental probability as a fraction, decimal or percentage. The value is always between 0 and 1.
Worked example
A drawing pin is dropped 80 times. It lands point-up 48 times. Find the experimental probability that it lands point-up.
P(point-up) = 48 ÷ 80 = 6 ÷ 10 = 3 ÷ 5 = 0.6.
So the experimental probability is 3/5 or 0.6.
More trials, better estimate
Experimental probability may be different each time we do the experiment, because it depends on the actual results. However, as the number of trials becomes very large, the experimental probability gets closer and closer to the true (theoretical) probability. This is why scientists repeat experiments many times.
Remember
- Experimental probability is based on results that really happened.
- It can change from experiment to experiment.
- More trials give a more reliable estimate.