using two fair dice, what is the probability of rolling a sum that exceeds 4?
number of ways to get 4 or less:
11, 12, 13, 21, 22, 31
prob of 4 or less = 6/36 = 1/6
prob of more than 4 = 5/6
To calculate the probability of rolling a sum that exceeds 4 with two fair dice, we need to determine the number of favorable outcomes (rolls that result in a sum greater than 4) and divide it by the total number of possible outcomes.
Step 1: Determine the total number of possible outcomes.
To find the total number of possible outcomes when rolling two dice, we multiply the number of outcomes for each die. Since each die has 6 faces, there are 6 * 6 = 36 possible outcomes.
Step 2: Identify the favorable outcomes.
Next, we need to determine the number of favorable outcomes, i.e., rolls that result in a sum greater than 4. We can do this by listing all the possible combinations and counting the favorable ones:
- (1, 4), (4, 1), (2, 3), (3, 2), (3, 4), (4, 3), (5, 2), (2, 5), (5, 3), (3, 5), (4, 5), (5, 4), and (6, 4), (4, 6), (6, 5), (5, 6), (6, 6)
There are 17 favorable outcomes.
Step 3: Calculate the probability.
To find the probability, divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 17 / 36 ≈ 0.4722
Therefore, the probability of rolling a sum that exceeds 4 with two fair dice is approximately 0.4722, or 47.22%.