## The Probability Distribution for the Score on Two Dice

If two fair dice are thrown, we can draw up the table below to represent the possible outcomes. The score shown in the body of the table is obtained by adding the scores on the two dice.

| Dice 2 | ||||||

Dice 1 | + | 1 | 2 | 3 | 4 | 5 | 6 |

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

2 | 3 | 4 | 5 | 6 | 7 | 8 | |

3 | 4 | 5 | 6 | 7 | 8 | 9 | |

4 | 5 | 6 | 7 | 8 | 9 | 10 | |

5 | 6 | 7 | 8 | 9 | 10 | 11 | |

6 | 7 | 8 | 9 | 10 | 11 | 12 |

From the table above, we can obtain the probability of obtaining a particular score by finding the number of occurrences of each score, as shown in the table below,

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |

Number of ways of obtaining a score of | 1 | 2 | 3 | 4 | 5 | 6 | 5 | 4 | 3 | 2 | 1 |

and dividing by the total number of possible outcomes, 36. We obtain the probability distribution in the table below.

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |