Probability

Probability is the measure of likelihood that an event will occur.

Words like "certain," "likely," and "impossible" can be used to describe the likelihood of an event.

Probability can also be quantified as a number between zero and one.

An event is impossible if it has a probability of 0. For example, rolling a "7" with a standard number cube is impossible and has a probability of 0.

An event is certain if it has a probability of 1. For example, rolling a number from 1 to 6 with a standard number cube is certain and has a probability of 1.

Events that are possible but not certain may have a probability that can be expressed as a fraction, decimal, or percentage. For example, the probability of rolling an even number with a standard number cube is 1/2 or 0.5 or 50%.

A sample space represents all possible outcomes of an experiment. The sample space can be organized in a list or a tree diagram.

Below is an example of an organized list and a tree diagram showing all of the combinations of three types of shorts, three types of shirts, and two types of shoes.

Using the 3 types of shorts, 3 types of shirts, and 2 types of shoes gives 18 different combinations of outfits. There are 18 different rows in the chart and 18 different branches on the far right of the tree diagram.

The Fundamental Counting Principle says that there are 3 x 3 x 2 = 18 possible combinations.

An organized list or tree diagram can be used to find the probability of a particular event occurring. Assuming that all the clothes are chosen at random, there is a 1/3 chance that the outfit will include a black shirt. Of the 18 possible combinations, 6 include a black shirt. The probability can be written as the fraction 6/18 -- simplified to 1/3.

When a probability experiment has very few trials, the results can be misleading. If a coin is flipped 10 times, it may come up 9 times as a head even though theoretical probability says it should come up heads half the time. The more times an experiment is done, the closer the experimental probability comes to the theoretical probability. If a coin is flipped 100 times, it will likely be heads close to 50 times, and if it is flipped 1,000 times, it is quite likely there will be around 500 heads tosses.