::: 3.03 Further on Probability :::
n order to make further and more complex calculations on probabilites, more properties need to be made known. For example, the union of two events is the "or" case - either event A or event B or both. Intersection is the "and" case - both. The conditional probability (P(B|A) - read "the probability of B given A") is defined by P(B|A) = P(A and B)/P(A).
Other fundamental rules of probability are:
- 0 < P(A) < 1
- P(S) = 1
- P(Ac) = 1 - P(A)
- P(A or B) = P(A) + P(B) - P(A and B)
- P(A and B) = P(A)P(B|A)
- If A and B are disjoint, then P(A and B) = 0. Because of this, P(A or B) = P(A) + P(B) for unions.
- A and B are independant when P(B|A) = P(B). Because of this, P(A and B) = P(A)P(B) for intersections.