- The formula for counting combinations is:
7.5 Basic Concepts of Probability
- For an experiment whose sample space consists of equally likely outcomes, the theoretical probability of the event is the ratio where and denote the number of outcomes in the event and in the sample space, respectively.
7.7 What Are the Odds?
- For an event ,
- If the odds in favor of are , then .
7.8 The Addition Rule for Probability
- If and are mutually exclusive events, then
- If and are events that contain outcomes of a single experiment, then
7.9 Conditional Probability and the Multiplication Rule
- If and are events associated with the first and second stages of an experiment, then .
7.10 The Binomial Distribution
- Suppose we have a binomial experiment with trials and the probability of success in each trial is . Then:
7.11 Expected Value
- If represents an outcome of an experiment and represents the value of that outcome, then the expected value of the experiment is:
where stands for the sum, meaning we add up the results of the formula that follows over all possible outcomes.