Keypoints

• the functions table() and prop.table() can be used effectively to calculate probabilities, joint probabilities and conditional probabilities on the basis of real data.

• values for $P(A^c)$, $P(A \cap B)$, $P(A \cup B)$ can often be obtained directly from the prop.table() output, but alternatively be calculated from other probabilities using the basic probability equations

• if a conditional probability ($P(A|B)$) is not directly available from data, it can be calculated with Bayes law $P(A|B)= \frac{P(B|A)P(A)}{P(B)}$