Probability has multiple approaches, each offering a different perspective on quantifying the chance of an event occurring.
Here’s an overview of three main approaches:
- Classical (or Mathematical or a priori) approach
- Relative frequency (or statistical or empirical) approach
- Subjective approach
‣ Classical (or Mathematical or a priori) approach:
The classical definition of probability is based on the assumption that all outcomes in a sample space are equally likely. It is expressed as the ratio of the number of favorable outcomes to the total number of possible outcomes.
According to calssical definition of probability, the probability of happening an event is calculated on the basis of logical reasoning and no trail is needed.
• It is not practicable in the field of statistics or Business.
Note: This drawback of classical definition is removed by next approach called relative frequency of occurrence.
Limitations:
- Assumes equal likelihood, which may not always be realistic in real-world scenarios.
- Applicable mainly to finite sample spaces.
‣ Relative frequency (or statistical or empirical) approach:
The statistical definition of probability is based on the concept of relative frequency. It involves conducting experiments or observations to determine the proportion of times an event occurs in the long run.
The main assumptions of empirical approach is as follow:
- Large number of trials made under similar and homogenous condition.
- The experiments are random. As there is no bias in favour of any outcome, all events enjoy equal chance of selection.
Limitations:
- Requires a large number of trials for accurate probability estimates, which may not always be feasible.
- Does not provide probabilities for one-time or unique events.
‣ Subjective Approach to Probability:
The subjective approach to probability is based on the idea that probability is a measure of an individual’s personal beliefs, judgments, or degree of confidence in the occurrence of an event.
• Instead of calculating probabilities based on frequencies or equally likely outcomes, it estimates them based on individual experiences, knowledge, and intuition.
• Subjective probability is also called personalistic approach to probability.
• It is very broad and highly flexible.
Odds in favour:
The odds in favor of an event represent the ratio of the probability of the event occurring to the probability of the event not occurring.
If the odds in favor of an event A are m:n, then probability of happeing and event A is given by
Q) The odds in favour of an event are 3:5. find the the probability of occurrence of this event?
solution:-
Odds against an event:
The odds against an event represent the ratio of the probability of the event not occurring to the probability of the event occurring.
If the odds against an event A are m:n, then probability of happeing and event A is given by
Q) The odds against an event are 4:7. find the the probability of occurrence of this event?
solution:-
