Probability

TL;DR

Quantifies how likely an event is to occur using a number between 0 (impossible) and 1 (certain).
Commonly expressed as a fraction or a percentage (for example, 1/2 or 50%).
Calculated as the number of desired outcomes divided by the total number of outcomes.

Definition

Probability is a branch of mathematics that deals with the likelihood of events occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that it is certain to happen.

Explanation

Probability measures the chances of specific outcomes within a given situation. It can be represented as a fraction, a percentage, or a decimal. The basic computation of probability uses the ratio of the number of desired outcomes to the total number of possible outcomes:

\text{Probability} = \frac{\text{Number of desired outcomes}}{\text{Total number of outcomes}}

Values close to 0 indicate low likelihood, while values close to 1 indicate high likelihood. Probability can be affected by conditions such as a weighted coin or the characteristics of the randomizing device.

Examples

Flipping a coin

When flipping a coin, there are two possible outcomes: heads or tails. The probability of getting heads is 1/2, or 50%. This means that if you flip a coin 100 times, you can expect to get heads 50 times and tails 50 times.

Using the formula:

P(\text{heads}) = \frac{1}{2} = 50\%

Rolling a die

When rolling a die, there are six possible outcomes: 1, 2, 3, 4, 5, or 6. The probability of rolling a 4 is 1/6, or 16.67%. This means that if you roll a die 100 times, you can expect to roll a 4 about 16 times.