1. **State the problem:** We have a game with three possible winnings: €0, €10, and €12. The angles for the corresponding sectors in the pie chart are 90°, 60°, and an unknown angle for €12. We need to complete the table with the missing angle and probabilities, then find the probability that Laura ends up neither winning nor losing money after playing twice. 2. **Find the missing angle:** The total angle in a circle is 360°. $$\text{Angle for } €12 = 360° - 90° - 60° = 210°$$ 3. **Calculate probabilities:** Probability is proportional to the angle divided by 360°. - For €0: $$P(0) = \frac{90°}{360°} = \frac{1}{4}$$ (given) - For €10: $$P(10) = \frac{60°}{360°} = \frac{1}{6}$$ - For €12: $$P(12) = \frac{210°}{360°} = \frac{7}{12}$$ 4. **Check probabilities sum:** $$\frac{1}{4} + \frac{1}{6} + \frac{7}{12} = \frac{3}{12} + \frac{2}{12} + \frac{7}{12} = \frac{12}{12} = 1$$ 5. **Find probability Laura neither wins nor loses money after two plays:** This means total winnings = €0 after two plays. Possible ways: - Win €0 both times. Probability: $$P(0,0) = P(0) \times P(0) = \left(\frac{1}{4}\right)^2 = \frac{1}{16}$$ 6. **Final answers:** - Missing angle for €12: 210° - Probability for €10: $\frac{1}{6}$ - Probability for €12: $\frac{7}{12}$ - Probability Laura neither wins nor loses money after two plays: $\frac{1}{16}$