# What is Probability

## Probability Problems

**Probability** is a numerical description of how likely an event is to occur or how likely it is that a proposition is true. Probability is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility and 1 indicates certainty.

A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes **Heads** and **Tails** are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either **Heads** or **Tails** is 1/2 (which could also be written as 0.5 or 50%).

## Formula

Probability of event to happen P(E) = | Number of favourable outcomes |

Total Number of outcomes |

Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of **Probability**

### Tossing a Coin

- head tails coin
- Tossing a Coin

When a coin is tossed, there are two possible outcomes

- heads (H) or
- tails (T)

We say that the probability of the coin landing H is 1/2 and the probability of the coin landing T is 1/2

### Throwing Dice

- pair of dice
- Throwing Dice

When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6. The probability of any one of them is 1/6.

## Formula

Probability of an event happening = | Number of ways it can happen |

Total number of outcomes |