Probability > Reasoning
1234Reasoning

Theory

Suppose you have a chance experiment in which you have charted all possible outcomes and that all outcomes have the same probability. For instance, the throwing of a dice with six equally probable outcomes. Assume the throwing happens randomly, you don't select, you don't consciously place a certain side up.

You can now calculate the probability of a certain outcome (say "5 pips") by dividing the number of favourable (or desired) outcomes by the total number of possible outcomes.

In this case we speak of the theoretical probability of an outcome. The number of favourable outcomes is always smaller than the the total number of outcomes. The theoretical probality therefore is a ratio with a value between 0 and 1.

The theoretical probability of 5 pips is Ρ ( X = 5 ) = 1 6 .

Here X represents the number of pips on the die.

Suppose you throw a die many times. The law of large numbers states that the empirical probability of 5 pips will approach the theoretical probability of 5 pips. So the empirical probability approaches 1 6 .
The law of large numbers connects empirical and theoretical probabilities. If you repeat an experiment often enough in the proper way, the relative frequency of a certain outcome approaches the theoretical probability of that outcome.

previous | next