## Probability

Probability
When two or more events are being considered, the likelihood that a specific event will occur is the probability of that event. Before determining the probability of an event, students must be able to find the total number of possible outcomes. The total number of possible outcomes can be found by making an organized list, by making a tree diagram, or by using multiplication. The fundamental counting principle states that if an experiment or problem has two steps and there are m possible choices or outcomes for the first step and n possible choices or outcomes for the second step, then the total number of possible choices or outcomes for both steps is m × n. For example, if you have 3 sizes of shirts and 2 choices of color, then for each of the three sizes there are two possible colors, so there are six possible outcomes in total because 3 × 2 = 6.

The result of an experiment is called an outcome. If the experiment is tossing a 1–6 number cube, then there are six possible outcomes, one for each face of the cube. An event is any collection of outcomes. Examples of events for tossing a number cube are that the number tossed is even, that the number is 1 or 2, or that the number is 3. The probability of an event is a measure of the likelihood that the event will occur. The probability is always a number between 0 and 1. A probability of 0 means that an event is impossible while a probability of 1 means that an event is certain.

When a coin is tossed, there are two outcomes, heads or tails. Either outcome is equally likely. When a 1–6 number cube is tossed, each face is equally likely to turn up. When a marble is chosen from a group of mixed marbles of the same size, without looking, each marble has the same chance of being chosen. Such outcomes are said to be equally likely outcomes. Sometimes the word fair is used as in fair coin or fair number cube. To indicate that each outcome is equally likely, the word random is used, such as in saying, “The object is chosen at random.”

The probability of an event is given by the ratio of the number of favorable outcomes to the number of possible outcomes. A favorable outcome is a way that the event could happen.

Teaching Model 20.2: Probability Concepts