Obviously, doing experiments takes time, so sometimes it is nice to calculate probabilities with doing an experiment.
We can do this if we know that all of the different outcomes of an experiment are equally likely. For instance, if we throw dice, we typically assume that each of the different numbers, 1, 2, 3, 4, 5 and 6, are equally likely to occur. So without doing any experiments we can say that the probability of rolling a 4 is 1/6. Effectively the same formula applies that we used before:
Let’s try some of these:
Now we can complete exercise 18C from pages 289 and 290 of the textbook:
Comparing experimental and theoretical probability
In general, when an experiment is performed many times, the probability that is calculated should tend towards the theoretical probability. It is unlikely that they will ever be exactly the same, but they can get so close that it is hard to tell the difference.
Let’s try question 1 of exercise 18D just to help us firm up this idea: