Details

• Day 1: Very simple, just write python code to sum the numbers between 1 and n.

• Day 2: Using Bayes’ Theorem to Calculate Posterior Probability

  Bayes’ Theorem Formula

  \[P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}\]

  Where:

  • $ P(A|B) $: The posterior probability of $ A $ given $ B $ (the probability of $ A $ after observing $ B $).
  • $ P(B|A) $: The likelihood (the probability of observing $ B $ given $ A $).
  • $ P(A) $: The prior probability of $ A $ (our initial belief about $ A $ before observing $ B $).
  • $ P(B) $: The marginal probability of $ B $ (the total probability of observing $ B $ under all possible scenarios).
    

    ⚠️ Warning: The prerequisite for using the law of total probability is that the events $ B_1, B_2, \dots, B_n $ are mutually exclusive (i.e., pairwise disjoint) and their union forms the entire sample space (i.e., they cover all possible outcomes).

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