Bayesian Updating and Random Variables

Important Formulae §

$$\begin{array}{rl}P(A|B)& =\frac{P(A\cap B)}{P(B)}\\ & \\ P(B|A)& =\frac{P(A|B)\cdot P(B)}{P(A)}\\ & \\ P(A)& =P(A|B)\cdot P(B)+P(A|S\backslash B)\cdot (1-P(B))\end{array}$$

Exercise Sheet §