Two different colored dice are rolled simultaneously. What is the probability of getting a sum of at least 5?

To solve this problem, we need to understand the total number of outcomes when two dice are rolled and the number of outcomes that result in a sum of at least 5.

Step 1: Total number of outcomes When two dice are rolled, each die has 6 faces. So, the total number of outcomes is 6*6 = 36.

Step 2: Favorable outcomes We need to find the number of outcomes that result in a sum of at least 5. This means we need to consider the sums of 5, 6, 7, 8, 9, 10, 11, and 12.

Here are the combinations:

• For a sum of 5: (1,4), (2,3), (3,2), (4,1)
• For a sum of 6: (1,5), (2,4), (3,3), (4,2), (5,1)
• For a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
• For a sum of 8: (2,6), (3,5), (4,4), (5,3), (6,2)
• For a sum of 9: (3,6), (4,5), (5,4), (6,3)
• For a sum of 10: (4,6), (5,5), (6,4)
• For a sum of 11: (5,6), (6,5)
• For a sum of 12: (6,6)

Counting these combinations, we get 4+5+6+5+4+3+2+1 = 30 favorable outcomes.

Step 3: Probability