If you roll a six-sided die, there are six possible outcomes,
and each of these outcomes is equally likely. A six is as
likely to come up as a three, and likewise for the other four
sides of the die. What, then, is the probability that a one
will come up? Since there are six possible outcomes, the
probability is *favorable outcomes* [link]. Given
that all outcomes are equally likely, we can compute the
probability of a one or a six using the formula:

The above formula applies to many games of chance. For
example, what is the probability that a card drawn at random
from deck of playing cards will be an ace? Since the deck has
four aces, there are four favorable outcomes; since the deck
has 52 cards, there are 52 possible outcomes. The probability
is therefore

Let's say you have a bag with 20 cherries, 14 sweet and 6
sour. If you pick a cherry at random, what is the probability
that it will be sweet? There are 20 possible cherries that
could be picked, so the number of possible outcomes is 20. Of
these 20 possible outcomes, 14 are favorable (sweet), so the
probability that the cherry will be sweet is

Here is a more complex example. You throw 2 dice. What is the probability that the sum of the two dice will be 6? To solve this problem, list all the possible outcomes. There are 36 of them since each die can come up one of six ways. The 36 possibilities are shown below.

Die 1 | Die 2 | Total | Die 1 | Die 2 | Total | Die 1 | Die 2 | Total |
---|---|---|---|---|---|---|---|---|

1 | 1 | 2 | 3 | 1 | 4 | 5 | 1 | |

1 | 2 | 3 | 3 | 2 | 5 | 5 | 2 | 7 |

1 | 3 | 4 | 3 | 3 | 5 | 3 | 8 | |

1 | 4 | 5 | 3 | 4 | 7 | 5 | 4 | 9 |

1 | 5 | 3 | 5 | 8 | 5 | 5 | 10 | |

1 | 6 | 7 | 3 | 6 | 9 | 5 | 6 | 11 |

2 | 1 | 3 | 4 | 1 | 5 | 6 | 1 | 7 |

2 | 2 | 4 | 4 | 2 | 6 | 2 | 8 | |

2 | 3 | 5 | 4 | 3 | 7 | 6 | 3 | 9 |

2 | 4 | 4 | 4 | 8 | 6 | 4 | 10 | |

2 | 5 | 7 | 4 | 5 | 9 | 6 | 5 | 11 |

2 | 6 | 8 | 4 | 6 | 10 | 6 | 6 | 12 |

You can see that 5 of the 36 possibilities total 6. Therefore,
the probability is

If you know the probability of an event
occurring, it is easy to compute the probability that the event
does not occur. If