|Probability Theory is the mathematical study of randomness. This theory deals with the possible outcomes of an event. It must be possible to list every outcome that can occur, and we must be able to state the expected relative frequencies of these outcomes. It is the method of assigning relative frequencies to each of the possible outcomes.|
|As it was mentioned
before, tossing a coin thousands of times would give a
probability of getting heads half of the time. In other
words, the observed proportion of heads becomes close to
½ (It is said that the probability of a head on any
single toss is ½). In intuitive terms it can be
concluded that probability is long-term relative
frequency. Having that in mind, correct probability
can only be determined by actually observing many tosses
of the coin to see if about ½ of the outcomes are heads.
We, however, can not observe a probability exactly,
simply because we could always continue tossing the coin.
Therefore, it can be concluded that mathematical
probability is an idealization based on imagining what
will happen to the relative frequencies in an indefinite
amount of trials.
|Long-term frequency is not the only way of interpreting probability. We can have a personal opinion about the next outcome of an event such as a coin toss. I can say that my personal probability of a head in the next toss is ½. Your personal probability may be different from mine. Personal probability sets us free from figuring out the outcome from many repetitions. Therefore, personal probability allows us to assign a probability to one-time events such as a golf tournament. Although we can have a personal probability about an event, we should also keep in mind the long-term relative frequency of chance.|