1. **Stating the problem:** We have a coin flip (2 outcomes: heads or tails) and a roll of a number cube (6 outcomes: numbers 1 through 6). We want to find: (a) Total number of outcomes. (b) Number of outcomes that do not involve rolling a 2. (c) Number of outcomes that involve heads and an odd number. 2. **Formula and rules:** The total number of outcomes when two independent events occur is the product of the number of outcomes for each event. 3. **Calculations:** (a) Total outcomes = number of coin outcomes × number of cube outcomes = $2 \times 6 = 12$ (b) Outcomes not involving rolling a 2 means the cube shows any number except 2, so 5 possible numbers (1,3,4,5,6). For each coin outcome, there are 5 such cube outcomes. Number of outcomes not involving 2 = $2 \times 5 = 10$ (c) Outcomes involving heads and an odd number. Odd numbers on the cube are 1, 3, 5 (3 numbers). Number of such outcomes = $1 \times 3 = 3$ 4. **Summary:** - Total outcomes: 12 - Outcomes without rolling 2: 10 - Outcomes with heads and odd number: 3 This completes the problem.