Statistics for Maintenance Modelling: Basic Probability Concepts

# Conditional Probability¤

The concept of conditional probability is one of the most important in all of probability theory. It's based on the notion that probabilities can be updated when certain events are observed. For instance if we are monitoring two components operating in parallel which share a common load, if one component fails, the probability of the other component failing increases as a result of the increased load placed on it. The updated probability of event E given that event F has occurred is the conditional probability of E given F has occurred and is written P(E|F).

## Independent and Dependent Events

When a coin is tossed twice, the two events are said to be independent, since the second flip of the coin is not influenced by the first flip. In short, two events are independent if the occurrence of one event does not effect the probability of the occurrence of the other. Two events E and F that are not independent are said to be dependent.

Events E and F are independent if and only if:

1. P(E|F) = P(E) assuming P(F) 0, or
2. P(F|E) = P(F) assuming P(E) 0, or
3. P(EF) = P(E) P(F)

Click here for an example.