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

7?

Verified step by step guidance

1. <span>Step 1: Understand the problem. We need to find the probability that the sum of the numbers on two six-sided dice equals 7.</span>
2. <span>Step 2: Determine the total number of possible outcomes when rolling two dice. Since each die has 6 sides, the total number of outcomes is 6 \times 6 = 36.</span>
3. <span>Step 3: Identify the successful outcomes where the sum of the numbers on the two dice equals 7. These pairs are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).</span>
4. <span>Step 4: Count the number of successful outcomes. There are 6 pairs that result in a sum of 7.</span>
5. <span>Step 5: Calculate the probability by dividing the number of successful outcomes by the total number of possible outcomes: \frac{6}{36}.</span>

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.