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Chapter 7: Probability
The following graphs show plots of the running proportion of students
with strep throats. Simulations were done for 200, 1,000, 10,000 and
500,000 trials. Observe that the proportion is converging to 0.22, the
theoretical probability of a student having strep throat. This illustrates
the concept of the
Law of Large Numbers
.
Figure 7-4:
Display of simulation for 200 trials
Since we are simulating the idea of the strep throat example, then the
probability of a student with strep throat will be 0.22. This is equal to the
theoretical probability of observing a student with strep throat. We should
expect as the number of trials increases, the proportion of observed students
with strep throat will approach 0.22. The simulation is graphically displayed
in
Figure 7-4
.