Probability — Part 2: Total probability and Bayes' theorem: visual lesson, CBSE Class 12 Mathematics

Lesson

Probability, Part 2: Total probability and Bayes' theorem

From causes to effects, and back again.

In this lesson you will

$P(W) = \frac{1}{2} \cdot \frac{5}{8} + \frac{1}{2} \cdot \frac{2}{8} = \frac{7}{16}$.

Concept

Diagram

$A$ is cut into $A \cap E_1$, $A \cap E_2$, $A \cap E_3$: add their probabilities.

Events $E_1, E_2, \ldots, E_n$ form a partition of $S$ if they are pairwise disjoint, their union is $S$ and each $P(E_i) > 0$ .