To determine the odds of rolling two number cubes (commonly known as dice) and achieving a sum of seven, we first need to assess the total number of possible outcomes when rolling two dice. Each die has six faces, so when rolling two dice, the total number of potential outcomes is 6 x 6, which equals 36.
Next, we should identify the combinations that will result in a sum of seven. The pairs of dice rolls that add up to seven are:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)
Counting these combinations, we find there are 6 different pairs that total seven. Therefore, the probability of rolling a sum of seven can be calculated by dividing the number of successful outcomes (6) by the total number of possible outcomes (36):
Probability = Number of Successful Outcomes / Total Outcomes = 6 / 36 = 1 / 6.
In terms of odds, which is a ratio of the probability of an event happening to the probability of it not happening, we can state the odds of rolling a sum of seven as:
Odds = Probability of Success / (1 – Probability of Success)
From our earlier calculation, the probability of rolling a sum of seven is 1/6 and thus the probability of not rolling a seven is 5/6. Therefore:
Odds = (1/6) / (5/6) = 1 / 5.
In conclusion, the odds of rolling two number cubes and getting a sum of seven are 1 to 5.