From: Bruce

Subject: math question

what is the probablity of rolling two dice and it coming out as seven?

a) 1/6

b) 1/36

please give me the correct awnser and explain please.

Hi Bruce

One way to approach a probability problem is to make a list or description of all the possible outcomes of the experiment, and then calculate the proportion of these possible outcomes satisfy the condition you are looking for, here that the sum is seven. To make this work you need to find a way to list the possible outcomes so that every item on the list has the same probability of occurring.

In the experiment of rolling two dice think of one as red and the other as green and list the possible result of the roll in a table. Here, for example, the (3,5) in third row and fifth column means a 3 was rolled on the red die and a 5 on the green die. As the table shows there are 36 possible outcomes.

1 | 2 | 3 | 4 | 5 | 6 | |
---|---|---|---|---|---|---|

1 | (1,1) | (1,2) | (1,3) | (1,4) | (1,5) | (1,6) |

2 | (2,1) | (2,2) | (2,3) | (2,4) | (2,5) | (2,6) |

3 | (3,1) | (3,2) | (3,3) | (3,4) | (3,5) | (3,6) |

4 | (4,1) | (4,2) | (4,3) | (4,4) | (4,5) | (4,6) |

5 | (5,1) | (5,2) | (5,3) | (5,4) | (5,5) | (5,6) |

6 | (6,1) | (6,2) | (6,3) | (6,4) | (6,5) | (6,6) |

For each of the possible outcomes add the numbers on the two dice and count how many times this sum is 7. If you do so you will find that the sum is 7 for 6 of the possible outcomes. Thus the sum is a 7 in 6 of the 36 outcomes and hence the probability of rolling a 7 is 6/36 = 1/6.

I hope this helps,

Harley

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