184 Fundamentals of Statistics
Early in the experiment, the relative frequency of heads jumps around
quite a bit, hovering above .5. As the number of tosses increases, the relative
frequency narrows to around the .5 level. The law of large numbers states
that as the number of replications increases, the relative frequency will ap-
proach the probability of the event, or, to put it another way, we can defi ne
the probability of an event as the value approached by the relative frequency
after an indefi nitely long series of trials.Probability Distributions
The pattern of probabilities for a set of events is called a probability distri-
bution. Probability distributions contain two important elements.- The probability of each event or combination of events must range from
0 to 1. - The total probability is 1.
In the coin-tossing example, there are two outcomes (head or tail), each
with a probability of .5. The sum of both events is 1, so this is an example
of a probability distribution. Probability distributions can be classifi ed into
two general categories: discrete and continuous.
Figure 5-1
The relative
frequency of
tossing a head
Figure 5-1 shows a chart of the results of tossing such a coin 5,000 times.