# Probability

**Probability** is about how **Likely** something is to occur,
or how likely something is true.

The mathematic probability is a **Number** between **0** and **1**.

0 indicates **Impossibility** and 1 indicates **Certainty**.

## The Probability of an Event

The probability of an event is:

The number of ways the event can happen / The number of possible outcomes.

**Probability = # of Ways / Outcomes**

## Tossing Coins

When tossing a coin, there are two possible outcomes:

Way | Probability |
---|---|

Heads | 1/2 = 0.5 |

Tails | 1/2 = 0.5 |

## P(A) - The Probability

The probability of an event **A** is often written as **P(A)**.

When tossing two coins, there are 4 possible outcomes:

Event | P(A) |
---|---|

Heads + Heads | 1/4 = 0.25 |

Tails + Tails | 1/4 = 0.25 |

Heads + Tails | 1/4 = 0.25 |

Tails + Heads | 1/4 = 0.25 |

## Throwing Dices

When throwing a dice, there are 6 possible outcomes:

Event | P(A) |
---|---|

Lands on 1 | 1/6 = 0.166666 |

Lands on 2 | 1/6 = 0.166666 |

Lands on 3 | 1/6 = 0.166666 |

Lands on 4 | 1/6 = 0.166666 |

Lands on 5 | 1/6 = 0.166666 |

Lands on 6 | 1/6 = 0.166666 |

The possibility of throwing 3 fours at the same time is

(1/6)^{3} (Lands on 4 to the power of 3):

The possibility of throwing 3 likes at the same time is 6 times larger:

(lands on 1) + (Lands on 2) + ... + (Lands on 6)

## 6 Balls

I have 6 balls in a bag: 3 reds, 2 are green, and 1 is blue.

Blindfolded. What is the probability that I pick a green one?

Number of **Ways** it can happen are 2 (there are 2 greens).

Number of **Outcomes** are 6 (there are 6 balls).

**Probability = Ways / Outcomes**

The probability that I pick a green one is 2 out of 6: 2/6 = 0.333333.

The probability is written P(green) = 0.333333.

P(A) | W/O | Probability |
---|---|---|

P(red) | 3/6 | 0.5000000 |

P(green) | 2/6 | 0.3333333 |

P(blue) | 1/6 | 0.1666666 |

## P(A) = P(B)

P(A) = P(B) | Event A and B have the same chance to occur |

P(A) > P(B) | Event A has a higher chance to occur |

P(A) < P(B) | Event A has a lower chance to occur |

For the 6 balls:

P(red) > P(green) | I am more likely to pick a red than a green |

P(red) > P(blue) | I am more likely to pick a red than a blue |

P(green) > P(blue) | I am more likely to pick a green than a blue |

P(blue) < P(green) | I am less likely to pick a blue than a green |

P(blue) < P(red) | I am less likely to pick a blue than a red |

P(green) < P(red) | I am less likely to pick a green than a red |

## Choosing a King

The probability of choosing a king in a deck of cards is 4 in 52.

Number of **Ways** it can happen are 4 (there are 4 kings).

Number of **Outcomes** are 52 (there are 52 cards).

**Probability = Ways / Outcomes**

The probability is 4 out of 52: 4/52 = 0.076923.

The probability is written P(king) = 0.076923.