Experimental probability

Two objective ways to estimate a probability:

• from evidence: do the experiment many times, or use past data;
• from theory: count equally likely outcomes (next lesson).

The words:

• the result of an experiment is an outcome;
• the set of all possible outcomes is the sample space, written in curly brackets: a coin {H, T}, a die {1, 2, 3, 4, 5, 6}.

Experimental probability = number of times the event happened ÷ total number of trials.

Example 2. Roll a die 50 times and get a 4 exactly 8 times. The experimental probability of a 4 is 8/50 = 0.16, or 16%. This is also called the relative frequency.

Try it yourself. Toss a paper cup 20 times and count how often it lands on its side, its top or its bottom. There is no way to work this out by reasoning: the only way to find the chances is by experiment.

Did you know? Snakes and Ladders began in India as Jñān-Chaupaḍ, a dice game for teaching values: the ladders stood for virtues, the snakes for vices.