3. Conditioning, Part 2

The law of total probability

This is a really important formula:

\[P(A) = \sum_{i=1}^{n} P(A \mid H_i) P(H_i)\]

We use this often in homework problems for finding the marginal probability of some event (\(P(A)\)). You will want to partition your sample space into mutually exclusive, exhaustive hypotheses (\(H_i\)). Try it out on some of the supplementary exercises!

Lecture errata

• There’s a mistake at 5:40: \(0.94\times 0.3 + 0.95\times 0.5 + 0.97\times 0.2\) equals \(0.951\), not \(0.957\).