A red and blue six-sided die are rolled. What is the probability that the red die shows a face greater than the blue die?
Nevermind, I solved the problem.
To find the probability that the red die shows a face greater than the blue die, we need to determine the possible outcomes and then calculate the probability of a favorable outcome.
Step 1: Determine the possible outcomes:
- Each die has six faces, so there are 6 * 6 = 36 possible outcomes when both dice are rolled.
Step 2: Identify the favorable outcomes:
- When the red die shows a face greater than the blue die, there are a total of 15 possible outcomes:
(Red - Blue)
2 - 1, 3 - 1, 4 - 1, 5 - 1, 6 - 1
3 - 2, 4 - 2, 5 - 2, 6 - 2
4 - 3, 5 - 3, 6 - 3
5 - 4, 6 - 4
6 - 5
There are 15 favorable outcomes in total.
Step 3: Calculate the probability:
- The probability is determined by dividing the number of favorable outcomes by the number of possible outcomes.
Probability = favorable outcomes / possible outcomes
Probability = 15 / 36
Simplifying the fraction gives:
Probability = 5 / 12
Therefore, the probability that the red die shows a face greater than the blue die is 5/12 or approximately 0.4167 (to four decimal places).