than our previous calculation of 4/9.
We can then make a calculation with a batter B who had hit 30 out of 90
at bats. This batter still has a batting average of ⅓. Probability calculated
in the same method gives 915/2093.
Batter C has an average of ⅓ with 333 hits in 999 times at bats. The
calculation results in 222111/500500.
Have you noticed? The probability is getting closer to our original
calculation, 4/9, as we increase the sample size. It shows that if we
infinitely increase the amount of hits and times at bat, the probability of
hitting one at three times at bat will reach 4/9. This pattern is called a law
of large numbers.
Law of large numbers is an essential law which connects mathematical
and statistical probability. Basically, it proves that when there are more
samples(experiments), the error made from calculations based on
statistical data are reduced.
If an experiment is n times repeated, say
rnis the amount of time an event A occurred. When the relative value
rnnreaches a specific value P, as n reaches infinity, P is the statistical
probability of event A happening.
P=nlim→∞rnn