Two different colored dice are rolled simultaneously.What is the probability of getting a sum of 8 or 4?

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 the sum of 8 or 4.

Step 1: Total 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 for Sum of 8 The pairs that give a sum of 8 when two dice are rolled are: (2,6), (3,5), (4,4), (5,3), and (6,2). So, there are 5 pairs. But since the dice are of different colors, each pair can occur in two ways. So, the total favorable outcomes for a sum of 8 is 5*2 = 10.

Step 3: Favorable Outcomes for Sum of 4 The pairs that give a sum of 4 when two dice are rolled are: (1,3), (2,2), and (3,1). So, there are 3 pairs. But since the dice are of different colors, each pair can occur in two ways. So, the total favorable outcomes for a sum of 4 is 3*2 = 6.

Step 4: Total Favorable Outcomes The total favorable outcomes for a sum of 8 or 4 is 10 (for 8) + 6 (for 4) = 16.

Step 5: Probability The probability of an event is the ratio of the number of favorable outcomes to the total number of outcomes. So, the probability of getting a sum of 8 or 4 when two different colored dice are rolled is 16/36 = 4/9.