Probability is a measure of how likely an event will occur. Mathematically, it is expressed as the ratio of the number of occurrences of the event to the number of all possible outcomes.

For example, the probability of getting a 3 when rolling a die is 1/6, since there are 6 possible outcomes (i.e 1,2,3,4,5 or 6) and only one of them is 3. The probability of getting an even number therefore is 3/6 = 1/2 since there are 3 possible outcomes which are even number (2,4,6).

The formula for probability of event $A$ is defined as follows:

$\mathbb{P}\left(A\right)=\frac{\text{Number of ways event}\phantom{\rule{3pt}{0ex}}A\phantom{\rule{3pt}{0ex}}\text{can happen}}{\text{Number of all possible outcomes}}$

The value of the probability of an event range from 0 to 1 (i.e. $0\le \mathbb{P}\le 1$). Probability value of 0 means the event is impossible and the probability value of 1 means the event is sure to happen.

Examples:

• The probability of getting a King when drawing a card from a deck of 52 playing card is 4/52.
• When tossing 2 coins, the probability of getting two heads (HH) is 1/4. The possible outcomes are HH, HT, TH, and TT. Only one of them is HH, hence the probability is 1/4.
• A bag contains 3 red balls, 2 yellow balls, and 5 green balls. If one ball is chosen at random, the probability that it is yellow is 2/10 = 1/5 = 0.2

Probability theory is applied in many fields such as finance, statistics, gambling, science, etc.