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| Two Types of Probability |
Two Types of Probability
The probability of an event can be determined using either a theoretical method or an experimental method.
The theoretical method
The theoretical method requires a detailed analysis of all the possible outcomes of an experiment. Once you can describe all of the possible outcomes, then you can state the theoretical probability of an ‘event A’ as: P(A) = Number of ways ‘event A’ can occur / Total number of outcomes.
With this definition you can calculate the theoretical probability of drawing a KING from the top of a deck of shuffled cards as P(KING) = 4 / 52, or 0.0769.
The experimental method
The experimental method requires a large number of trials. Using the same example, in order to find the experimental probability of drawing a KING you would shuffle a deck of cards, turn over the top card and note whether it was a KING or not. Then you would repeat the experiment a large number of times. Finally you would calculate the probability as:
P(KING) = Number of times a KING was drawn / Total number of draws. What constitutes a ‘large number of times’? You can calculate the experimental probability after each trial, and continue making additional trials until the probability settles down to a relatively constant number. For example, after just 10 trials you may have found no KINGs, or several KINGs, and the experimental value would vary considerably from one trial to the next. But after a few hundred trials, the value of P(KING) would change very little after each additional trial.
The beauty of the system is that if your analysis of the situation is correct, and if your experiments are carried out correctly, then as you conduct more trials the value of the experimental probability approaches the value of the theoretical probability. The system is self-checking.
The probability of an event can be determined using either a theoretical method or an experimental method.
The theoretical method
The theoretical method requires a detailed analysis of all the possible outcomes of an experiment. Once you can describe all of the possible outcomes, then you can state the theoretical probability of an ‘event A’ as: P(A) = Number of ways ‘event A’ can occur / Total number of outcomes.
With this definition you can calculate the theoretical probability of drawing a KING from the top of a deck of shuffled cards as P(KING) = 4 / 52, or 0.0769.
The experimental method
The experimental method requires a large number of trials. Using the same example, in order to find the experimental probability of drawing a KING you would shuffle a deck of cards, turn over the top card and note whether it was a KING or not. Then you would repeat the experiment a large number of times. Finally you would calculate the probability as:
P(KING) = Number of times a KING was drawn / Total number of draws. What constitutes a ‘large number of times’? You can calculate the experimental probability after each trial, and continue making additional trials until the probability settles down to a relatively constant number. For example, after just 10 trials you may have found no KINGs, or several KINGs, and the experimental value would vary considerably from one trial to the next. But after a few hundred trials, the value of P(KING) would change very little after each additional trial.
The beauty of the system is that if your analysis of the situation is correct, and if your experiments are carried out correctly, then as you conduct more trials the value of the experimental probability approaches the value of the theoretical probability. The system is self-checking.
