Two dice are rolled. Find the odds that the score on the dice is either 7 or 12
To find the odds of rolling a specific sum on two dice, we need to determine the number of favorable outcomes and the total number of possible outcomes.
First, let's calculate the total number of possible outcomes. When rolling two dice, we have 6 possible outcomes for each die, resulting in a total of 6 x 6 = 36 possible outcomes.
Next, we need to determine the number of favorable outcomes, i.e., the number of combinations that result in a sum of either 7 or 12.
For a sum of 7, there are a total of 6 favorable outcomes: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). Notice that we count each combination only once, so we do not count (6, 1) and (1, 6) separately.
For a sum of 12, there is only one favorable outcome, which is (6, 6).
Therefore, the number of favorable outcomes is 6 (for a sum of 7) + 1 (for a sum of 12) = 7.
Now, we can calculate the odds by dividing the number of favorable outcomes by the total number of possible outcomes:
Odds = Number of favorable outcomes / Total number of possible outcomes
Odds = 7 / 36
Thus, the odds of scoring either 7 or 12 when rolling two dice is 7/36.
Imagine that the dice are numbered A and B. There are 36 possible results. Six of the combinations add up to 7
A---B
1 & 6
2 & 5
3 % 4
4 & 3
5 & 2
6 & 1
and only one combination (6 & 6) adds up to 12.
What does that tell you?