What is the probability of rolling a sum of 3 on a standard pair of six-sided dice? Express your answer as a fraction or a decimal number rounded to three decimal places, if necessary.
Answer (2)
The probability of rolling a sum of 3 on a standard pair of six-sided dice is 18 1 or approximately 0.056. This means there are 2 favorable outcomes out of 36 possible outcomes. Understanding this probability can help in games involving dice by assessing chances of specific outcomes.
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Find the total possible outcomes: 6 × 6 = 36 .
Identify favorable outcomes (sum of 3): (1, 2) and (2, 1).
Calculate the probability: 36 2 = 18 1 .
Express as a decimal: 0.056 .
Explanation
Understand the problem When rolling a pair of six-sided dice, we want to find the probability that the sum of the numbers rolled is 3.
List all possible outcomes Let's list all possible outcomes when rolling two six-sided dice. The first die can have values from 1 to 6, and the second die can also have values from 1 to 6. The total number of possible outcomes is 6 × 6 = 36 .
Identify favorable outcomes Now, let's identify the outcomes where the sum of the two dice is equal to 3. The possible outcomes are (1, 2) and (2, 1). So, there are 2 favorable outcomes.
Calculate the probability The probability of rolling a sum of 3 is the number of favorable outcomes divided by the total number of possible outcomes. Therefore, the probability is 36 2 = 18 1 .
Express as a decimal To express the probability as a decimal rounded to three decimal places, we can divide 1 by 18: 18 1 ≈ 0.056 .
State the final answer The probability of rolling a sum of 3 on a standard pair of six-sided dice is 18 1 , which is approximately 0.056.
Examples
This type of probability calculation is used in many games involving dice, such as board games or casino games. Understanding the likelihood of certain outcomes helps players make informed decisions and strategize effectively. For example, in a game where rolling a sum of 3 allows you to advance, knowing the probability ( 18 1 or about 5.6%) helps you assess your chances and plan your moves accordingly.
