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Experimental Probability

Flip a coin $10$ times and note down the result. Though you have an equal chance of getting either side, do you always get $5$ heads and $5$ tails out of $10$ trials?

Or, roll a die $60$ times and make a note of how many times you get a six. Will you always roll a six $10$ times?

In both cases, the answer is No!

Though the theoretical probability of getting heads in the first example is $\frac{1}{2}$ , and the theoretical probability of rolling a six in the second example is $\frac{1}{6}$ , you may not get heads exactly $\frac{1}{2}$ the time, and you may not roll a six exactly $\frac{1}{6}$ of the time.

Suppose that, out of $60$ rolls of the die, you roll a six $7$ times. The fraction $\frac{7}{60}$ is called the experimental probability . That is, the experimental probability of an event is the ratio of the number of favorable outcomes to the total number of trials.

With a fair coin or a fair die, you know the theoretical probability ahead of time. Experimental probability is useful in situations where you don't or can't know the probability of an outcome.