Calculating Probability

Probability can be written in three equivalent forms: a fraction (3/10), a decimal (0.3), or a percentage (30%). Pick the form the question asks for. To convert, divide the fraction to get the decimal, then multiply by 100 to get the percentage. All three forms describe the same chance.

The probability scale runs from 0 to 1, or from 0% to 100%. A probability of 0 means the event is impossible. A probability of 1 means the event is certain. A probability of 0.5 means the event is just as likely to happen as not. Higher values mean the event is more likely.

An outcome is one specific result you could get from a chance event, such as picking the third red ball from a bag. An event is a collection of outcomes you care about, such as drawing any red ball. So an event can contain one outcome or many outcomes from the same chance situation.

Theoretical probability uses the formula "desired outcomes divided by total outcomes" when each outcome is equally likely. Experimental probability estimates the answer by running trials and counting how often the event actually happened. Theoretical gives the exact value; experimental gives an estimate that improves with more trials.

Experimental probabilities depend on what happened during a limited number of trials, so they may not match the true probability exactly. For example, the true probabilities could be 40% red and 60% blue, while 100 trials might give 37% red and 63% blue. The more trials you run, the more accurate your estimate becomes.

Imagine a bag with 10 balls: 3 red and 7 blue. If you draw one ball at random, the probability of picking red is 3 out of 10, or 30%. This simple bag example shows how counting desired outcomes and total outcomes gives a clear probability you can express as a fraction, decimal, or percentage.