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**:-