Question

if you roll two fair dice (one black die and one white die), in how many ways can you obtain a sum of at least 3? a sum of at least 3 can be obtained in different ways.

Explanation:

Step1: Calculate total number of outcomes

When rolling two dice, each die has 6 possible outcomes. By the fundamental counting principle, the total number of outcomes is \(6\times6 = 36\).

Step2: Calculate number of outcomes with sum less than 3

The minimum sum of two dice is 2 (1 on black die and 1 on white die). There is only 1 way to get a sum of 2: \((1,1)\).

Step3: Calculate number of outcomes with sum at least 3

Use the complement rule. Subtract the number of non - desired outcomes (sum less than 3) from the total number of outcomes. So the number of ways to get a sum of at least 3 is \(36−1=35\).

Answer:

35