Risk Assessment: Tools, Techniques, and Their Applications

7.4 Conditional Probability

Conditional probability is a probability whose sample space has been limited to only those outcomes that fulfill a certain condition. It is expressed as

which is the probability of event A given event B.

Events can be categorized into two main categories, single event and compound event. A single event is when you only expect one event to occur such as flipping coins or rolling dice. It could even be drawing a certain card, such as the ace of spades, from a deck of 52 cards.

A compound event is when two or more events or things are happening. Frequently, we want to know the probability of two things happening. In other words, one thing happens and then the other thing happens. Since “and” means multiply, the probability of one event must be multiplied by the probability of another event happening. An example of this would be flipping two heads in a row. The expression would be .

Generally speaking, when working with probability, “and” means to multiply and “or” means to add. However, you must be careful. Here are three important rules for compound probabilities:

1. If A and B are independent, or the occurrence of one does not affect the other, then P(A and B) = P(A) × (B).

2. If A and B are dependent, or the occurrence of one does affect the other, then ...