A First Course in Statistics, 12th Edition

3.5 Conditional Probability

The event probabilities we’ve been discussing give the relative frequencies of the occurrences of the events when the experiment is repeated a very large number of times. Such probabilities are often called unconditional probabilities because no special conditions are assumed other than those that define the experiment.

Often, however, we have additional knowledge that might affect the outcome of an experiment, so we may need to alter the probability of an event of interest. A probability that reflects such additional knowledge is called the conditional probability of the event. For example, we’ve seen that the probability of observing an even number (event A) on a toss of a fair die is ${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$. But suppose we’re given ...