Approaches to Probability 🎓
There are different schools of thought on how to define probability.
1. Classical / Mathematical Approach 🏛️
Based on the assumption that outcomes are equally likely. This is the "Priori" probability (calculated before the experiment).
- Formula:
P(A) = Favorable Cases / Total Exhaustive Cases - Limitation: Fails if outcomes are not equally likely (e.g., a biased coin).
- Example: Tossing a fair coin P(H) = 1/2.
2. Relative Frequency / Empirical Approach 📊
Based on actual experiments performed many times. This is the "Posteriori" probability (calculated after observing).
- Logic: If you flip a coin 1000 times and get Heads 520 times,
P(H) ≈ 0.52. - As the number of trials increases, it approaches the Classical probability.
- Application: Life expectancy tables, accident rates.
3. Subjective Approach 🧠
Based on beliefs, experience, and intuition of an individual.
- Example: A manager saying "I am 80% sure this product will succeed."
- Useful in business decisions where no past data exists.
4. Axiomatic Approach (Modern) 📐
Proposed by Kolmogorov. It defines probability as a function satisfying three axioms:
P(A) ≥ 0(Non-negativity)P(S) = 1(Total probability is 1)- If A and B are mutually exclusive,
P(A ∪ B) = P(A) + P(B).
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