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:

There are three basic terms of probability: experiment, sample space, and event. An experiment is a process by which an observation, or outcome, is obtained. A sample space means the set (S) of all possible outcomes of an experiment. An event means any subset (E) of the sample space. The events are subsets of S, but they are not outcomes. When an event is certain, the E = S, like rolling a number between 1 and 6 [E = 1, 2, 3, 4, 5, 6} = S], this is called a certain event. If you were to say, the event to roll a 7, since the events are subsets of the sample space and 7 is not contained in the sample set, we say this is an impossible event. Obviously, only one die is used for this event.