What is the probability of rolling a sum of 5 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 5 on two six-sided dice is 9 1 , or approximately 0.111 . This is calculated by finding the favorable outcomes and dividing them by the total possible outcomes. There are 4 combinations that yield a sum of 5 out of 36 total outcomes.
;
Determine the total possible outcomes: 6 × 6 = 36 .
Identify favorable outcomes (sum to 5): (1, 4), (2, 3), (3, 2), (4, 1) - a total of 4.
Calculate the probability: 36 4 = 9 1 .
Express as a decimal rounded to three places: 0.111 .
Explanation
Understand the problem We are rolling a pair of standard six-sided dice and want to find the probability that the sum of the numbers rolled on the two dice is equal to 5.
Total possible outcomes Let's list all the possible outcomes when rolling two six-sided dice. Each die has 6 faces, so there are a total of 6 × 6 = 36 possible outcomes.
Favorable outcomes Now, let's identify the outcomes where the sum of the two dice is equal to 5. These are: (1, 4), (2, 3), (3, 2), (4, 1) So, there are 4 favorable outcomes.
Calculate the probability The probability of rolling a sum of 5 is the number of favorable outcomes divided by the total number of possible outcomes: P ( sum of 5 ) = Total number of possible outcomes Number of favorable outcomes = 36 4 = 9 1 As a decimal rounded to three decimal places, this is approximately 0.111.
Final Answer The probability of rolling a sum of 5 on a standard pair of six-sided dice is 9 1 , which is approximately 0.111.
Examples
Consider a game where you win if you roll a sum of 5 with two dice. Knowing the probability (approximately 0.111) helps you understand your chances of winning each time you roll. This kind of probability calculation is useful in many games involving dice or other random events, allowing you to assess risks and make informed decisions.
