If two six-sided dice are rolled, what is the probability that the total number of spots showing is

7?

Key Concepts

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a ratio of favorable outcomes to the total number of possible outcomes. In the context of rolling dice, it quantifies how often a specific total, such as 7, can be achieved compared to all possible outcomes when two dice are rolled.

Sample Space

The sample space is the set of all possible outcomes of a random experiment. For rolling two six-sided dice, the sample space consists of 36 combinations (6 sides on the first die multiplied by 6 sides on the second die), which helps in calculating the probability of specific outcomes like rolling a total of 7.

Favorable Outcomes

Favorable outcomes refer to the specific results that satisfy the condition of the probability question. In this case, the favorable outcomes for rolling a total of 7 with two dice include the combinations (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), totaling six combinations that contribute to the desired outcome.