1. **Stating the problem:** Jessica wants to know how many winners to expect on Monday if there are 750 contestants, based on previous days' data. 2. **Understanding the data:** From the table: - Friday: 215 contestants, 27 winners - Saturday: 417 contestants, 54 winners - Sunday: 368 contestants, 39 winners 3. **Calculate the winning probability for each day:** Friday: $$\frac{27}{215} \approx 0.1256$$ Saturday: $$\frac{54}{417} \approx 0.1295$$ Sunday: $$\frac{39}{368} \approx 0.1060$$ 4. **Calculate the average winning probability:** $$\frac{0.1256 + 0.1295 + 0.1060}{3} = \frac{0.3611}{3} \approx 0.1204$$ 5. **Use the average probability to estimate Monday winners:** Expected winners = probability \times number of contestants $$0.1204 \times 750 = 90.3$$ 6. **Interpretation:** Jessica should expect about 90 winners on Monday. 7. **Regarding the coin flip:** - Theoretical probability of heads in one flip is $$\frac{1}{2} = 0.5$$ - Experimental probability from 10 flips with 8 heads is $$\frac{8}{10} = 0.8$$ 8. **Reason for difference:** Experimental probability varies due to the small number of trials and randomness, while theoretical probability assumes infinite trials and perfect fairness. 9. **Summary:** - Expected winners on Monday: 90 - Difference in coin flip probabilities explained by experimental vs theoretical definitions.