Relative Frequency in Probability

Relative Frequency (A Posteriori)

Definition:

• Relative frequency, also known as empirical probability or a posteriori probability, is the probability of an event based on the number of times it has occurred in the past.
• It is a measure of the frequency of occurrence of an event in a large number of trials.

Key Concepts:

• Long-run relative frequency: The proportion of times an event occurs in a large number of trials.
• Law of Large Numbers (LLN): States that as the number of trials increases, the relative frequency of an event will approach its true probability.

Calculation:

• Relative frequency is calculated as the number of times an event occurs (successes) divided by the total number of trials.
• Formula: Relative Frequency = (Number of Successes) / (Total Number of Trials)

Example:

• A coin is flipped 100 times, and heads come up 55 times.
• Relative frequency of getting heads = 55/100 = 0.55

Interpretation:

• The relative frequency is a measure of how often an event occurs in the long run.
• It provides an estimate of the true probability of an event, which is unknown.
• As the number of trials increases, the relative frequency becomes a more accurate estimate of the true probability.

Advantages:

• Relative frequency is based on actual data and is a more objective measure of probability.
• It is useful for estimating probabilities in situations where the true probability is unknown.

Limitations:

• Relative frequency is sensitive to the number of trials and can be affected by chance fluctuations.
• It may not accurately reflect the true probability of an event, especially with small sample sizes.