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clarifying the transition between statements #481

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clarifying the transition between statements #481

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6 changes: 6 additions & 0 deletions Statistical_Inference/ConditionalProbability/lesson
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Expand Up @@ -58,6 +58,12 @@
- Class: text
Output: Suppose we don't know P(A) itself, but only know its conditional probabilities, that is, the probability that it occurs if B occurs and the probability that it occurs if B doesn't occur. These are P(A|B) and P(A|~B), respectively. We use ~B to represent 'not B' or 'B complement'.

- Class: text
Output: Since B and ~B are by definition disjoint sets, we can add the probabilities of the two subsets, P(A|B) and P(A|~B), to give the probability of A.

- Class: text
Output: Then we can rewrite P(A) = P(A|B) + P(A|~B) using our initial conditional probability statement, P(A|B) = P(A&B) / P(B), as well as the same for P(A|~B).

- Class: text
Output: We can then express P(A) = P(A|B) * P(B) + P(A|~B) * P(~B) and substitute this is into the denominator of Bayes' Formula.

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