Probability estimate, Classical & Frequency approach

Probability is a measure how likely outcomes of a particular experiment or activity will result.

1. CLASSICAL APPROACH
All possible outcomes are are equally likely.
2. FREQUENCY APPROACH
If after 𝑛 trials of an experiment, 𝒏 is very large, an event 𝐸 occurs in ℎ of these, then 𝑃(𝐸)=ℎ/𝑛.

Law of large numbers states that as the number of trials increases, the relative frequency obtained tends towards the theoretical probability.
Axiom 1: For every event 𝐴,
𝑃(𝐴)≥0
Axiom 2: For the sure or certain event 𝐴,
𝑃(𝐴)=1
Axiom 3: For any number of mutually exclusive events 𝐴_1,𝐴_2,…,
𝑃(𝐴_1∪𝐴_2∪…)=𝑃(𝐴_1 )+𝑃(𝐴_2 )+…

Sample space is a set of all possible outcomes.
𝑆={𝐻𝐻,𝐻𝑇,𝑇𝐻,𝑇𝑇}

Event: A subset of Sample Space.
𝐸={𝐻𝑇,𝑇𝐻}

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