Explanation:
First, you need to know some terms related to probability. When working with probability, a random action or series of actions is called a trial. An outcome is the result of a trial, and an event is a particular collection of outcomes. Events are usually described using a common characteristic of the outcomes.
Let's apply this language to see how the terms work in practice. Some games require rolling a die with six sides, numbered from 1 to 6. (Dice is the plural of the die.) The chart below illustrates the use of trial, outcome, and event for such a game:
Trial
Outcomes
Examples of Events
Rolling a die
There are 6 possible outcomes:
{1, 2, 3, 4, 5, 6}
Rolling an even number: {2, 4, 6}
Rolling a 3: {3}
Rolling a 1 or a 3: {1, 3}
Rolling a 1 and a 3: { } (Only one number can be rolled, so this outcome is impossible. The event has no outcomes in it.)
Notice that a collection of outcomes is put in braces and separated by commas.
A simple event is an event with only one outcome. Rolling a 1 would be a simple event because there is only one outcome that works—1! Rolling more than a 5 would also be a simple event because the event includes only 6 as a valid outcome. A compound event is an event with more than one outcome. For example, in rolling one six-sided die, rolling an even number could occur with one of three outcomes: 2, 4, and 6.
When you roll a six-sided die many times, you should not expect any outcome to happen more often than another (assuming that it is a fair die). The outcomes in a situation like this are said to be equally likely. It’s very important to recognize when outcomes are equally likely when calculating probability. Since each outcome in the die-rolling trial is equally likely, you would expect to get each outcome of the rolls. That is, you'd expect the rolls to be 1, of the rolls to be 2, of the rolls to be 3, and so on.
A spinner is divided into four equal parts, each colored with a different color as shown below. When this spinner is spun, the arrow points to one of the colors. Are the outcomes equally likely?
A) Yes, they are equally likely.
B) No, they are not equally likely.
Answer:
All the outcomes are equally likely. Each color provides a different outcome, and each color takes up the circle. You would expect the arrow to point to each color of the time.